(adsbygoogle = window.adsbygoogle || []).push({}); ** The problem statement, all variables and given/known data

1/

set S = set of the multiples of any two natural numbers a, b

S = {n in N such that a|n and b|n}

2/

Denote min(S) = LCM(a,b) = least common multiple of a and b

From previous result, I already proved that :

If a divides c and if b divides d, then GCD(a,b) divides GCD(c,d)

Now the question isto prove: LCM(a,b) divides LCM(c,d)

** My thoughts:

By definition of set S, x = LCM(a,b) satisfies the fact that a|n and b|n for n in N

I think, y = LCM(c,d) satisfies set S when c|m and d|m for m in N

But after that, I get confused on what to do next.

I think of trying to prove: LCM(c,d) = k * LCM(a,b), but I'm not sure if this is the right direction, or I need to do something else.

Could someone please give me on hints on what to do? Thank you in advance.

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# Proof that LCM(c,d) divides LCM(a,b), known GCD(a,b) divides GCD(c,d)

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