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The prime factorization of 32 is 2x2x2x2x2 or 25. The prime factorization of 40 is 2x2x2x5 or 23x5. For a number to be a multiple of a given number the multiple must have the entire prime factorization of that number in is. So a multiple of 32 must contain 2x2x2x2x2 or 25 . Likewise a multiple of 40 must contain 2x2x2x5 or 23x5. The least number that this could possible happen with must have 5 factors of 2 and one factor of 5 (the highest exponent on each individual prime factor). Thus the LCM is 2x2x2x2x2x5 or 25x5 Which is 160.

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Q: LCM with prime factorization of 32 and 40?
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