HCF and LCM Competitive Exams
50 questions · Mathematics
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Question 1 of 50
Find the largest 3-digit number divisible by 6, 8 and 12.
ExplanationLCM = 24. Since 999 ÷ 24 gives quotient 41, the number is 24×41 = 984.
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Question 2 of 50
Find the HCF of 408 and 1032.
ExplanationEuclid: 1032 = 2×408 + 216; 408 = 1×216 + 192; 216 = 1×192 + 24; 192 = 8×24. HCF = 24.
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Question 3 of 50
Find the HCF of 36 and 84.
Explanation36 = 2²×3² and 84 = 2²×3×7, so HCF = 2²×3 = 12.
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Question 4 of 50
Find the LCM of the co-prime numbers 8 and 15.
ExplanationFor co-prime numbers LCM = product = 8×15 = 120.
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Question 5 of 50
Find the HCF of 2/3, 8/9, 16/81 and 10/27.
ExplanationHCF of fractions = HCF of numerators ÷ LCM of denominators = 2 ÷ 81.
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Question 6 of 50
Milk containers hold 403 L, 434 L and 465 L. The maximum capacity of a measure that can measure each quantity exactly is:
Explanation403 = 13×31, 434 = 14×31, 465 = 15×31, so HCF = 31.
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Question 7 of 50
Find the HCF of 156 and 234.
Explanation156 = 2²×3×13 and 234 = 2×3²×13, so HCF = 2×3×13 = 78.
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Question 8 of 50
Find the least number which when divided by 6, 9, 15 and 18 leaves remainder 4 in each case.
ExplanationLCM = 90, so number = 90 + 4 = 94.
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Question 9 of 50
The sum of two numbers is 36, their HCF is 4 and their LCM is 48. The sum of their reciprocals is:
ExplanationProduct = 4×48 = 192. Sum of reciprocals = (a+b)/ab = 36/192 = 3/16.
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Question 10 of 50
Find the HCF of 3/4, 9/16 and 15/32.
ExplanationHCF of numerators (3, 9, 15) = 3; LCM of denominators (4, 16, 32) = 32; so HCF = 3/32.
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Question 11 of 50
Find the LCM of 0.6, 9.6 and 0.12.
ExplanationWrite as 60, 960 and 12 (×0.01). LCM = 960, so the answer is 9.60.
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Question 12 of 50
Find the largest number which divides 62, 132 and 237 leaving the same remainder in each case.
ExplanationHCF of the differences (70, 175) = 35. Remainder is 27 each time.
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Question 13 of 50
Find the greatest length of tape that can measure exactly 3 m 15 cm, 4 m 20 cm and 5 m 25 cm.
ExplanationHCF(315, 420, 525) = 105 cm.
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Question 14 of 50
Find the HCF of 0.63, 1.05 and 2.1.
ExplanationWrite as 63, 105, 210 (×0.01). HCF = 21, so the answer is 0.21.
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Question 15 of 50
The HCF of two numbers is 23 and the other factors of their LCM are 13 and 14. The larger number is:
ExplanationNumbers are 23×13 = 299 and 23×14 = 322. The larger is 322.
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Question 16 of 50
Find the LCM of 16, 24, 36 and 54.
ExplanationHighest powers: 2⁴ and 3³, so LCM = 16×27 = 432.
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Question 17 of 50
A floor is 15 m 17 cm long and 9 m 2 cm wide. The side of the largest square tile that exactly covers it is:
ExplanationHCF(1517, 902) = 41 cm.
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Question 18 of 50
Three bells toll at intervals of 12, 15 and 20 seconds. If they toll together at the start, after how many minutes will they next toll together?
ExplanationLCM(12, 15, 20) = 60 seconds = 1 minute.
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Question 19 of 50
Find the LCM of 3/8, 9/16 and 15/32.
ExplanationLCM of numerators (3, 9, 15) = 45; HCF of denominators (8, 16, 32) = 8; so LCM = 45/8.
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Question 20 of 50
The HCF of two numbers is 11 and their LCM is 693. If one number is 77, the other is:
ExplanationOther = (11×693) ÷ 77 = 99.
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Question 21 of 50
Find the LCM of 2/5, 4/15 and 6/25.
ExplanationLCM of numerators (2, 4, 6) = 12; HCF of denominators (5, 15, 25) = 5; so LCM = 12/5.
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Question 22 of 50
Find the LCM of 2/3, 4/9 and 5/6.
ExplanationLCM of fractions = LCM of numerators ÷ HCF of denominators = 20 ÷ 3.
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Question 23 of 50
Two numbers are in the ratio 2 : 3 and their HCF is 8. Their LCM is:
ExplanationNumbers are 16 and 24. LCM = 16×24 ÷ 8 = 48.
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Question 24 of 50
Find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively.
ExplanationHCF(285−9, 1249−7) = HCF(276, 1242) = 138.
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Question 25 of 50
Find the least number which when divided by 8, 12 and 15 leaves remainders 5, 9 and 12 respectively.
ExplanationEach divisor minus remainder is 3, so number = LCM − 3 = 120 − 3 = 117.
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Question 26 of 50
Find the least number which when divided by 12, 15, 20 and 54 leaves remainder 8 in each case.
ExplanationLCM = 540, so number = 540 + 8 = 548.
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Question 27 of 50
Find the HCF of 1/2, 3/4 and 5/6.
ExplanationHCF of numerators (1, 3, 5) = 1; LCM of denominators (2, 4, 6) = 12; so HCF = 1/12.
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Question 28 of 50
Three runners take 40 s, 60 s and 90 s to complete one round of a circular track. If they start together, they will meet again at the start after:
ExplanationLCM(40, 60, 90) = 360 s = 6 minutes.
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Question 29 of 50
Three ropes of 42 m, 63 m and 84 m are cut into equal pieces of the greatest possible length. The length of each piece is:
ExplanationHCF(42, 63, 84) = 21 m. This gives 2 + 3 + 4 = 9 pieces.
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Question 30 of 50
The HCF and LCM of two numbers are 12 and 240. If one number is 48, the other is:
ExplanationProduct of numbers = HCF×LCM, so other = (12×240)÷48 = 60.
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Question 31 of 50
Three traffic lights change after every 48 s, 72 s and 108 s. If they change together at 8:00:00 am, they will next change together at:
ExplanationLCM(48, 72, 108) = 432 s = 7 min 12 s.
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Question 32 of 50
Two numbers are in the ratio 3 : 4 and their LCM is 120. Their sum is:
ExplanationNumbers are 3x and 4x, LCM = 12x = 120, so x = 10. Numbers are 30 and 40; sum = 70.
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Question 33 of 50
Find the HCF of 144, 180 and 252.
ExplanationCommon prime powers are 2² and 3², so HCF = 4×9 = 36.
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Question 34 of 50
Find the smallest 4-digit number divisible by 12, 15, 20 and 27.
ExplanationLCM = 540. Smallest 4-digit multiple of 540 = 540×2 = 1080.
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Question 35 of 50
Find the LCM of 1.2 and 1.8.
ExplanationWrite as 12 and 18 (×0.1). LCM = 36, so the answer is 3.6.
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Question 36 of 50
Boys can be arranged exactly in rows of 12, 18 or 24. The least number of boys is:
ExplanationLCM(12, 18, 24) = 72.
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Question 37 of 50
Find the smallest 5-digit number divisible by 12, 18 and 21.
ExplanationLCM = 252. 10000 ÷ 252 gives about 39.7, so the next whole multiple is 252×40 = 10080.
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Question 38 of 50
Find the least number which, when increased by 6, is exactly divisible by 24, 32, 36 and 54.
ExplanationLCM = 864, so number = 864 − 6 = 858.
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Question 39 of 50
Find the LCM of 12, 18 and 24.
Explanation12 = 2²×3, 18 = 2×3², 24 = 2³×3, so LCM = 2³×3² = 72.
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Question 40 of 50
Find the largest number which divides 245 and 1029 leaving remainder 5 in each case.
ExplanationHCF(240, 1024) = 16.
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Question 41 of 50
Buses leave a stand together at 6:00 am and then every 20, 25 and 30 minutes respectively. They will next leave together at:
ExplanationLCM(20, 25, 30) = 300 min = 5 hours, so 6:00 am + 5 h = 11:00 am.
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Question 42 of 50
Find the least number which leaves remainder 1 when divided by 5, 6, 8, 9 or 12 but is exactly divisible by 13.
ExplanationLCM = 360, so the number is 360k + 1. Testing k = 1, 2, … the first that is divisible by 13 is k = 10, giving 3601 = 13×277.
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Question 43 of 50
The product of the HCF and LCM of 24 and 36 is:
ExplanationHCF×LCM = product of the numbers = 24×36 = 864.
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Question 44 of 50
The HCF of two consecutive natural numbers is:
ExplanationConsecutive numbers are co-prime, so their HCF is always 1.
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Question 45 of 50
Find the HCF of 1.2, 1.8 and 3.0.
ExplanationWrite as 12, 18, 30 (×0.1). HCF = 6, so the answer is 0.6.
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Question 46 of 50
The product of two numbers is 2028 and their HCF is 13. Their LCM is:
ExplanationLCM = product ÷ HCF = 2028 ÷ 13 = 156.
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Question 47 of 50
Find the greatest 4-digit number divisible by 15, 25, 40 and 75.
ExplanationLCM = 600. 9999 ÷ 600 gives quotient 16, so the number is 600×16 = 9600.
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Question 48 of 50
The LCM of two numbers is 14 times their HCF. The sum of HCF and LCM is 600. If one number is 280, the other is:
ExplanationHCF + 14×HCF = 600 gives HCF = 40, LCM = 560. Other = (40×560) ÷ 280 = 80.
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Question 49 of 50
Find the LCM of 15, 20, 25 and 30.
ExplanationHighest powers: 2², 3 and 5², so LCM = 4×3×25 = 300.
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Question 50 of 50
Four bells toll at intervals of 12, 15, 20 and 30 seconds. After how many seconds will they toll together again?
ExplanationLCM(12, 15, 20, 30) = 60.
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