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117 as a product of primes is 3 times 3 times 13. 65 is 5 times 13. Both will divide every number that is a product of 3 times 3 times 5 times 13 and any other integer, i.e., every product of 585, including 585, 1170, 1755, etc. Of course this includes 65 times 117 or 7605. The smallest number that both divide is 585.
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