Competition problem — Number theory

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Number theory Difficulty 1.7 Junior Find the answer

What is the smallest positive integer that is a multiple of each of 3, 5, 7, and 9?

Your answer

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

Solution

Since 9 is a multiple of 3, every positive integer that is a multiple of 9 is also a multiple of 3. The smallest positive integer that is a multiple of each of 7 and 9 is 63. The smallest multiple of 63 that is also a multiple of 5 is 315.

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