Three numbers are in the ratio \(3:2:13\), and their LCM is 2574. Their HCF is:
33
Since 3, 2 and 13 are pairwise coprime, let the three numbers be \(3k,\ 2k,\ 13k\) where \(k\) is their HCF.
The LCM of \(3k,2k,13k\) equals \(k\times \operatorname{lcm}(3,2,13) = k\times 78 = 78k\).
Set \(78k = 2574\), giving \(k = \dfrac{2574}{78} = 33\).
Hence, the HCF of the three numbers is 33.
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Important Questions from LCM and HCF
The HCF and LCM of two numbers are 12 and 72, respectively. If the ratio of the two numbers is 2 ∶ 3, then the larger of the two numbers is:
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Joseph visits the club on every 5 th day, Harsh visits on every 24 th day, while Sumit visits on every 9 th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again?
What is the least number which when divided by 12,20 and 24 leaves in each case a remainder of 8?
Which of the following is a pair of co-primes?
