G.C.D. vs L.C.M.
Number Theory
Level
1
True or false :
The lowest common multiple of 2 positive integers is always a multiple of their greatest common divisor .
Yes, always!
No, never!
Maybe
Not enough information
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1 solution
Let a , b be positive integers, c = L C M ( a , b ) and d = G C D ( a , b ) . Then, by definition, d ∣ a , so a = d m , for some integer m . Also, a ∣ c , thus, c = a k , for some integer k . Therefore, c = k d m , and as k m is an integer, then d ∣ c .