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How old is Samuel?

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He's 22 correct? If you divide his age by 2 (the only even prime number) and add four, you get 15 which is the  LCM of 3 and 5

22 appears correct. If you let his age be S, then divide by the only even prime (2) and add four, it's equal to the LCM of of 5 and 3 (15), so:

S/2 + 4 = 15