24.
A multiple of (x), for example, is a number divisible by x.
So multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48 ...etc.
Multiples of 8 are 8, 16, 24, 32, 40, 48 ...etc.
Since the lowest multiple which 3 and 8 have in common is "24", it is called the "LCM" (a.k.a. Lowest Common Multiple). 48 is a common multiple shared by 3 and 8, but it is not the lowest.
This is essentially a mathematical / analytical proof, so I hope it helps.
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Least Common Multiple (LCM) for 46 3 is 138
The least common multiple of 3 4 and 10 is 6060
The least common multiple of 2 , 3 , 20 = 60
The least common multiple of 4 , 3 , 6 = 12
The least common multiple of 3 , 8 , 13 = 312