{
  "title": "HCF and LCM using Prime Factorisation - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Find HCF of 12 and 18 using prime factorisation.", "options": {"A": "4", "B": "6", "C": "8", "D": "9"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "Find LCM of 12 and 18 using prime factorisation.", "options": {"A": "24", "B": "30", "C": "36", "D": "42"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "HCF of 15 and 25 using prime factors:", "options": {"A": "3", "B": "5", "C": "10", "D": "15"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "LCM of 15 and 25 using prime factors:", "options": {"A": "50", "B": "60", "C": "75", "D": "90"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "HCF of 21 and 35:", "options": {"A": "5", "B": "7", "C": "9", "D": "11"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "LCM of 21 and 35:", "options": {"A": "70", "B": "84", "C": "98", "D": "105"}, "correct_answer": "D"},
    {"id": 7, "difficulty": "easy", "question": "HCF of 24 and 36:", "options": {"A": "8", "B": "10", "C": "12", "D": "14"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "LCM of 24 and 36:", "options": {"A": "60", "B": "72", "C": "84", "D": "96"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "HCF of 28 and 42:", "options": {"A": "7", "B": "14", "C": "21", "D": "28"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "LCM of 28 and 42:", "options": {"A": "56", "B": "70", "C": "84", "D": "98"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "HCF of 45 and 60:", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "LCM of 45 and 60:", "options": {"A": "120", "B": "150", "C": "180", "D": "210"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "HCF of 54 and 72:", "options": {"A": "9", "B": "12", "C": "18", "D": "24"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "LCM of 54 and 72:", "options": {"A": "144", "B": "162", "C": "216", "D": "270"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "HCF of 75 and 90:", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "LCM of 75 and 90:", "options": {"A": "150", "B": "225", "C": "300", "D": "450"}, "correct_answer": "D"},
    {"id": 17, "difficulty": "easy", "question": "HCF of 84 and 96:", "options": {"A": "6", "B": "12", "C": "18", "D": "24"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "LCM of 84 and 96:", "options": {"A": "336", "B": "420", "C": "504", "D": "672"}, "correct_answer": "D"},
    {"id": 19, "difficulty": "easy", "question": "HCF of 100 and 125:", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "D"},
    {"id": 20, "difficulty": "easy", "question": "LCM of 100 and 125:", "options": {"A": "250", "B": "300", "C": "400", "D": "500"}, "correct_answer": "D"},
    
    {"id": 21, "difficulty": "medium", "question": "Find HCF of 120, 150 and 180.", "options": {"A": "10", "B": "15", "C": "20", "D": "30"}, "correct_answer": "D"},
    {"id": 22, "difficulty": "medium", "question": "Find LCM of 120, 150 and 180.", "options": {"A": "600", "B": "900", "C": "1200", "D": "1800"}, "correct_answer": "D"},
    {"id": 23, "difficulty": "medium", "question": "HCF of 144, 180 and 192:", "options": {"A": "6", "B": "12", "C": "18", "D": "24"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "LCM of 144, 180 and 192:", "options": {"A": "1440", "B": "2160", "C": "2880", "D": "4320"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "Find HCF of 210, 315 and 420.", "options": {"A": "15", "B": "21", "C": "35", "D": "105"}, "correct_answer": "D"},
    {"id": 26, "difficulty": "medium", "question": "Find LCM of 210, 315 and 420.", "options": {"A": "840", "B": "1260", "C": "1680", "D": "2520"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "HCF of 240, 300 and 360:", "options": {"A": "30", "B": "40", "C": "50", "D": "60"}, "correct_answer": "D"},
    {"id": 28, "difficulty": "medium", "question": "LCM of 240, 300 and 360:", "options": {"A": "1200", "B": "1800", "C": "2400", "D": "3600"}, "correct_answer": "D"},
    {"id": 29, "difficulty": "medium", "question": "Find HCF of 275, 350 and 425.", "options": {"A": "5", "B": "15", "C": "25", "D": "35"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "Find LCM of 275, 350 and 425.", "options": {"A": "3850", "B": "5950", "C": "7350", "D": "9350"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "HCF of 324, 432 and 540:", "options": {"A": "36", "B": "54", "C": "72", "D": "108"}, "correct_answer": "D"},
    {"id": 32, "difficulty": "medium", "question": "LCM of 324, 432 and 540:", "options": {"A": "2160", "B": "3240", "C": "4320", "D": "6480"}, "correct_answer": "D"},
    {"id": 33, "difficulty": "medium", "question": "Find HCF of 385, 490 and 595.", "options": {"A": "5", "B": "7", "C": "35", "D": "49"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "Find LCM of 385, 490 and 595.", "options": {"A": "5390", "B": "10780", "C": "16170", "D": "21560"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "HCF of 441, 567 and 693:", "options": {"A": "21", "B": "42", "C": "63", "D": "84"}, "correct_answer": "C"},
    {"id": 36, "difficulty": "medium", "question": "LCM of 441, 567 and 693:", "options": {"A": "43659", "B": "52398", "C": "65448", "D": "78529"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Find HCF of 504, 588 and 672.", "options": {"A": "28", "B": "42", "C": "56", "D": "84"}, "correct_answer": "D"},
    {"id": 38, "difficulty": "medium", "question": "Find LCM of 504, 588 and 672.", "options": {"A": "14112", "B": "21168", "C": "28224", "D": "35280"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "HCF of 600, 750 and 900:", "options": {"A": "50", "B": "75", "C": "100", "D": "150"}, "correct_answer": "D"},
    {"id": 40, "difficulty": "medium", "question": "LCM of 600, 750 and 900:", "options": {"A": "3000", "B": "4500", "C": "6000", "D": "9000"}, "correct_answer": "D"},
    {"id": 41, "difficulty": "medium", "question": "Find HCF of 1260, 1440 and 1620.", "options": {"A": "60", "B": "90", "C": "120", "D": "180"}, "correct_answer": "D"},
    {"id": 42, "difficulty": "medium", "question": "Find LCM of 1260, 1440 and 1620.", "options": {"A": "90720", "B": "120960", "C": "151200", "D": "181440"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "HCF of 1320, 1540 and 1760:", "options": {"A": "110", "B": "132", "C": "154", "D": "220"}, "correct_answer": "D"},
    {"id": 44, "difficulty": "medium", "question": "LCM of 1320, 1540 and 1760:", "options": {"A": "18480", "B": "27720", "C": "36960", "D": "55440"}, "correct_answer": "D"},
    {"id": 45, "difficulty": "medium", "question": "Find HCF of 1400, 1750 and 2100.", "options": {"A": "50", "B": "100", "C": "150", "D": "350"}, "correct_answer": "D"},
    {"id": 46, "difficulty": "medium", "question": "Find LCM of 1400, 1750 and 2100.", "options": {"A": "10500", "B": "21000", "C": "31500", "D": "42000"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "HCF of 1512, 1764 and 2016:", "options": {"A": "42", "B": "63", "C": "84", "D": "126"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "medium", "question": "LCM of 1512, 1764 and 2016:", "options": {"A": "42336", "B": "63504", "C": "84672", "D": "127008"}, "correct_answer": "D"},
    {"id": 49, "difficulty": "medium", "question": "Find HCF of 1650, 1925 and 2200.", "options": {"A": "25", "B": "55", "C": "75", "D": "275"}, "correct_answer": "D"},
    {"id": 50, "difficulty": "medium", "question": "Find LCM of 1650, 1925 and 2200.", "options": {"A": "23100", "B": "46200", "C": "69300", "D": "92400"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "If HCF(18,24)=6, find LCM(18,24).", "options": {"A": "36", "B": "48", "C": "60", "D": "72"}, "correct_answer": "D"},
    {"id": 52, "difficulty": "medium", "question": "If LCM(15,20)=60, find HCF(15,20).", "options": {"A": "3", "B": "5", "C": "10", "D": "15"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "If HCF(28,42)=14, find LCM(28,42).", "options": {"A": "56", "B": "70", "C": "84", "D": "98"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "medium", "question": "If LCM(36,48)=144, find HCF(36,48).", "options": {"A": "6", "B": "9", "C": "12", "D": "18"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "medium", "question": "If HCF(54,72)=18, find LCM(54,72).", "options": {"A": "144", "B": "162", "C": "216", "D": "288"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "medium", "question": "If LCM(75,90)=450, find HCF(75,90).", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "medium", "question": "If HCF(84,96)=12, find LCM(84,96).", "options": {"A": "336", "B": "420", "C": "504", "D": "672"}, "correct_answer": "D"},
    {"id": 58, "difficulty": "medium", "question": "If LCM(100,125)=500, find HCF(100,125).", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "D"},
    {"id": 59, "difficulty": "medium", "question": "If HCF(120,150)=30, find LCM(120,150).", "options": {"A": "300", "B": "450", "C": "600", "D": "750"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "If LCM(144,180)=720, find HCF(144,180).", "options": {"A": "12", "B": "18", "C": "24", "D": "36"}, "correct_answer": "D"},
    {"id": 61, "difficulty": "medium", "question": "Product of two numbers is 2160, HCF is 12. Find LCM.", "options": {"A": "120", "B": "150", "C": "180", "D": "210"}, "correct_answer": "C"},
    {"id": 62, "difficulty": "medium", "question": "Product of two numbers is 1575, LCM is 315. Find HCF.", "options": {"A": "3", "B": "5", "C": "7", "D": "9"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "HCF of two numbers is 16, LCM is 480. If one number is 96, find other.", "options": {"A": "60", "B": "70", "C": "80", "D": "90"}, "correct_answer": "C"},
    {"id": 64, "difficulty": "medium", "question": "LCM of two numbers is 180, HCF is 12. If one number is 36, find other.", "options": {"A": "48", "B": "54", "C": "60", "D": "72"}, "correct_answer": "C"},
    {"id": 65, "difficulty": "medium", "question": "Product of two numbers is 2028, HCF is 13. Find LCM.", "options": {"A": "126", "B": "144", "C": "156", "D": "168"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "LCM of two numbers is 2310, HCF is 11. If one number is 110, find other.", "options": {"A": "201", "B": "211", "C": "221", "D": "231"}, "correct_answer": "D"},
    {"id": 67, "difficulty": "medium", "question": "HCF of two numbers is 25, LCM is 300. If one number is 75, find other.", "options": {"A": "80", "B": "90", "C": "100", "D": "110"}, "correct_answer": "C"},
    {"id": 68, "difficulty": "medium", "question": "Product of two numbers is 2601, HCF is 17. Find LCM.", "options": {"A": "143", "B": "153", "C": "163", "D": "173"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "LCM of two numbers is 504, HCF is 6. If one number is 42, find other.", "options": {"A": "60", "B": "66", "C": "72", "D": "78"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "HCF of two numbers is 18, product is 12960. Find LCM.", "options": {"A": "540", "B": "630", "C": "720", "D": "810"}, "correct_answer": "C"},
    {"id": 71, "difficulty": "medium", "question": "Two numbers are in ratio 3:4, HCF is 15. Find LCM.", "options": {"A": "120", "B": "150", "C": "180", "D": "210"}, "correct_answer": "C"},
    {"id": 72, "difficulty": "medium", "question": "Two numbers are in ratio 5:7, LCM is 140. Find HCF.", "options": {"A": "2", "B": "4", "C": "6", "D": "8"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "Two numbers are in ratio 4:5, HCF is 12. Find numbers.", "options": {"A": "36,45", "B": "40,50", "C": "44,55", "D": "48,60"}, "correct_answer": "D"},
    {"id": 74, "difficulty": "medium", "question": "Two numbers are in ratio 9:11, LCM is 297. Find HCF.", "options": {"A": "3", "B": "6", "C": "9", "D": "12"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Two numbers are in ratio 8:9, product is 2592. Find HCF.", "options": {"A": "6", "B": "9", "C": "12", "D": "18"}, "correct_answer": "D"},
    {"id": 76, "difficulty": "medium", "question": "Two numbers are in ratio 7:8, HCF is 15. Find sum of numbers.", "options": {"A": "195", "B": "210", "C": "225", "D": "240"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "Two numbers are in ratio 6:7, LCM is 168. Find difference.", "options": {"A": "2", "B": "4", "C": "6", "D": "8"}, "correct_answer": "B"},
    {"id": 78, "difficulty": "medium", "question": "Two numbers are in ratio 5:6, HCF is 14. Find product.", "options": {"A": "5880", "B": "6720", "C": "7560", "D": "8400"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "Two numbers are in ratio 11:13, LCM is 429. Find sum.", "options": {"A": "60", "B": "66", "C": "72", "D": "78"}, "correct_answer": "C"},
    {"id": 80, "difficulty": "medium", "question": "Two numbers are in ratio 3:5, product is 2160. Find LCM.", "options": {"A": "120", "B": "144", "C": "168", "D": "192"}, "correct_answer": "A"},
    
    {"id": 81, "difficulty": "hard", "question": "For what value of n, HCF(25,15+n)=5?", "options": {"A": "n=5k", "B": "n not multiple of 5", "C": "n even", "D": "n odd"}, "correct_answer": "B"},
    {"id": 82, "difficulty": "hard", "question": "Find greatest number dividing 230, 350 and 480 leaving remainder 5 each.", "options": {"A": "15", "B": "25", "C": "35", "D": "45"}, "correct_answer": "D"},
    {"id": 83, "difficulty": "hard", "question": "Find least number divisible by 12, 15 and 20.", "options": {"A": "60", "B": "90", "C": "120", "D": "150"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Greatest number dividing 70, 125 and 165 leaving remainders 5,8,9 respectively.", "options": {"A": "13", "B": "17", "C": "19", "D": "23"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "Least number which when divided by 6,9,12,15 leaves remainder 3 each.", "options": {"A": "183", "B": "186", "C": "189", "D": "192"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "Greatest number dividing 285 and 1249 leaving remainders 9 and 7 respectively.", "options": {"A": "23", "B": "46", "C": "69", "D": "92"}, "correct_answer": "B"},
    {"id": 87, "difficulty": "hard", "question": "Least number divisible by 8,12,18 and leaves remainder 5.", "options": {"A": "72", "B": "77", "C": "144", "D": "149"}, "correct_answer": "B"},
    {"id": 88, "difficulty": "hard", "question": "Greatest 4-digit number divisible by 12, 15 and 18.", "options": {"A": "9900", "B": "9936", "C": "9960", "D": "9990"}, "correct_answer": "D"},
    {"id": 89, "difficulty": "hard", "question": "Smallest 5-digit number divisible by 16, 24 and 36.", "options": {"A": "10000", "B": "10032", "C": "10080", "D": "10128"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "Greatest number dividing 398, 436 and 542 leaving remainders 7,11,15 respectively.", "options": {"A": "13", "B": "17", "C": "23", "D": "31"}, "correct_answer": "B"},
    {"id": 91, "difficulty": "hard", "question": "Find smallest square number divisible by 8, 12 and 15.", "options": {"A": "900", "B": "1200", "C": "1600", "D": "3600"}, "correct_answer": "D"},
    {"id": 92, "difficulty": "hard", "question": "Find least perfect square divisible by 3, 4, 5 and 6.", "options": {"A": "900", "B": "1200", "C": "1600", "D": "3600"}, "correct_answer": "D"},
    {"id": 93, "difficulty": "hard", "question": "Find greatest 3-digit number divisible by 8, 10 and 12.", "options": {"A": "960", "B": "980", "C": "990", "D": "995"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "Find smallest number which when increased by 17 is divisible by 520 and 468.", "options": {"A": "4663", "B": "4673", "C": "4683", "D": "4693"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Three bells ring at 12, 18 and 24 minute intervals. They ring together at noon. When next together?", "options": {"A": "1:12 PM", "B": "1:24 PM", "C": "1:36 PM", "D": "1:48 PM"}, "correct_answer": "C"},
    {"id": 96, "difficulty": "hard", "question": "Find least number of square tiles for room 15m×9m.", "options": {"A": "12", "B": "15", "C": "18", "D": "21"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "Find greatest length to measure 42m, 49m and 63m exactly.", "options": {"A": "7m", "B": "14m", "C": "21m", "D": "28m"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "Find least number which when divided by 20,25,35,40 leaves remainder 14,19,29,34 respectively.", "options": {"A": "1394", "B": "1395", "C": "1396", "D": "1397"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "Find smallest 4-digit number divisible by 18, 24 and 32.", "options": {"A": "1152", "B": "1200", "C": "1248", "D": "1296"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "Find greatest number dividing 148, 246 and 623 leaving remainders 4,6 and 11 respectively.", "options": {"A": "12", "B": "18", "C": "24", "D": "36"}, "correct_answer": "D"}
  ]
}