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Class 10 HCF and LCM — practice questions with answers

Number Systems · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Find the HCF of 12 and 18.
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Answer: A) 6
12 = 2² x 3, 18 = 2 x 3². Common factors: 2 x 3 = 6.
2. The HCF of two numbers is 1. Their LCM is 143. If one number is 11, the other is:
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Answer: A) 13
Product = HCF x LCM = 1 x 143 = 143. Other = = 13.
3. The HCF and LCM of two numbers are 12 and 336 respectively. If one of the numbers is 84, find the other number.
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Answer: A) 48
Product = HCF x LCM = 12 x 336 = 4032. Other number = = 48.
4. Two cyclists start together at the same point of a velodrome track in Indore. One completes a lap in 39 seconds and the other in 52 seconds.
After how long do they meet again at the starting point, and how many laps has the faster cyclist completed by then?
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Answer: C) 156 seconds; 4 laps
They meet at the start after LCM(39, 52) seconds. 39 = 3 x 13 and 52 = 2² x 13, so LCM = 2² x 3 x 13 = 156 s. The faster cyclist takes 39 s per lap, so he has done 156 / 39 = 4 laps. Using the HCF, 13 s, describes no meeting at all; 39 x 52 = 2028 over-counts because the lap times are not co-prime; dividing 156 by 52 gives the slower cyclist's 3 laps.
5. Two numbers have HCF 11 and LCM 1694, and both numbers lie between 100 and 200.
Which pair is it?
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Answer: C) 121 and 154
Write the numbers as 11a and 11b with a, b co-prime; LCM = 11ab = 1694 gives ab = 154 = 2 x 7 x 11. For both numbers to lie between 100 and 200, a and b must lie between 10 and 18, and (a, b) = (11, 14) works, giving 121 and 154. The pair 11 and 1694 does have HCF 11 and LCM 1694 but lies outside the stated range; 132 and 143 give LCM 1716; 110 and 154 give HCF 22, not 11.
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