Three numbers are in the ratio 17 : 13 : 8, and their LCM is 7072. Their HCF is:
4
Let the HCF of the three numbers be \(k\). Then the three numbers are \(17k\), \(13k\), and \(8k\).
Since 17, 13, and 8 are pairwise coprime (no common factors), the LCM of \(17k\), \(13k\), \(8k\) is \(k \times 17 \times 13 \times 8 = 1768k\).
Setting \(1768k = 7072\): \(k = \frac{7072}{1768} = 4\).
Verification: the three numbers are 68, 52, 32; their LCM is indeed 7072.
Hence, the HCF of the three numbers is 4.
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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.
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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?
