Competition problem — Number theory

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Number theory Difficulty 5.3 AIME, harder Find the answer

Example 7 Find the least common multiple of 108, 28, and 42.

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

Since
$108=2^{2} \times 3^{3}, 28=2^{2} \times 7, 42=2 \times 3 \times 7$

we get
$\{108,28,42\}=2^{2} \times 3^{3} \times 7=756$

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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.