The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:

Correct answer: 322

Solution

When two numbers have HCF 23, they can be written as \(23a\) and \(23b\), where \(a\) and \(b\) are coprime. Since the other factors of the LCM are 13 and 14, the numbers are \(23\times 13\) and \(23\times 14\). The larger number is 322.

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