Three numbers are in the ratio 5 : 14 : 9, and their LCM is 7560. Their HCF is:
12
Let the three numbers be \(5k\), \(14k\) and \(9k\), where \(k\) is the common factor.
Since \(5\), \(14\) and \(9\) are pairwise co-prime, the LCM of the three numbers is \(k \times 5 \times 14 \times 9 = 630k\).
Given \(630k = 7560\), so \(k = \frac{7560}{630} = 12\).
Because \(5\), \(14\) and \(9\) have no common factor, the HCF of the numbers equals \(k = 12\).
Hence, their HCF is \(12\).
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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?
