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Divisible question for the experts

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Hey guys,

Just starting to get into quant studies and I came across a stumper. The question states, "if j is divisible by 12 and 10, is j divisible by 24"

I created prime boxes for 12 and 10 and deduced it had to be since 3x2x2x2 = 24.

However my Manhattan GMAT book states it cannot be determined since there are only two 2's that are definitely in the prime factorization of j because the 2 in the prime factorization of 10 may be redundant as one of the 2's in the prime factorization of 12.

I have to admit, I don't follow that at all. Any assistance would be greatly appreciated.

Thanks!

I should note, I can't believe how much math I have forgotten. I need the basic refresher imaginable...

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