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Ambar Mitra
Lowest Common Multiple
by Factorization
What is “Lowest Common Multiple” (LCM)?
Let's say we have two numbers, 8 and 14.
The multiples of 8 are
8 , 16 , 24 , 32 , 40 , 48 , 56 , 64 , 72 , 80
The multiples of 14 are
14 , 28 , 42 , 56 , 70 , 84 , 98 , 112 , 126 , 140
We find that the lowest number that is common in these two lists is 56.
The Lowest Common Multiple of 8 and 14 is 56
Determining the LCM
Example-1: Find LCM of 8 and 14
Write all factors of 8 : 2 , 2 , 2
Write all factors of 14 : 2 , 7
Make combined list of factors, including the common factors (blue highlight) only
once:
2,2,2,7
Multiply the factors to get LCM = 56
Example-2: Find LCM of 18 and 27
Write all factors of 18 : 2, 3 , 3
Write all factors of 14 : 3 , 3 , 3
Make combined list of factors, including the common factors (blue and orange
highlights) only once:
2,3,3,3
Multiply the factors to get LCM = 54