Akbar Birbal marbles

Let Akbar and Birbal have n marbles, where n>0.

Akbar says to Birbal, "If I give you some marbles you will have twice as many as I will have." Birbal says to Akbar, "If I give you some marbles you will have thrice as many as I will have."

What is the minimum possible value of n for which the above statements are true?

Solution:
Suppose Akbar gives Birbal some marbles leaving Akbar with k marble and Birbal with 2k marbles. This implies that n=k+2k for some integer k i.e. n is divisible by 3.

Similarly, after Birbal gives Akbar some marbles leaving Birbal with m marbles and Akbar with 3m marbles, we have that n=m+3m=4m for some integer m, i.e. n is divisible by 4.

So minimum value of n = LCM(3,4) = 12.

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