Question 19

If the LCM of two numbers is 12 times their HCF and the sum of LCM and HCF is 403, and one number is 93, find the other number.

Solution

Let the other number be A, the LCM be L, and the HCF be H.

The LCM of two numbers is 12 times their HCF. Thus, $$L=12H$$

The sum of LCM and HCF is 402. Thus -

$$L+H=403$$
$$13H=403$$
$$H=31$$
Therefore, $$L=12H=12\times31=372$$

We know that the product of two numbers is the product of their LCM and the HCF.

$$93\times A=L\times H$$

$$93\times A=372\times31$$

$$A=124$$

Thus, the other number is 124.

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