Competition problem — Number theory

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Number theory Difficulty 5.2 AIME, harder Find the answer

I2.4 If the least common multiple (L.C.M.) of 76 and $d$ is 456 and the highest common factor (H.C.F.) of 76 and $d$ is $c$ , determine the value of the positive integer $d$ .
If the least common multiples (L.C.M.) of 76 and $d$ is 456 and the highest common factor (H.C.F.) of 76 and $d$ is $c$ , determine the value of the positive integer $d$ .

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

$\begin{array}{l}76 \times d=\text { L.C.M. } \times \text { H.C.F. }=456 \times 4 \\ d=24\end{array}$

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.