Answer :

Let us understand what L.C.M, Least Common Multiple is.

Least common multiple of two or more integers, is the smallest positive integer that is divisible by these two or more integers.


In order to find L.C.M, we need to find factors of each terms.


Factorization of 4a2b4c = 2 × 2 × a × a × b × b × b × b × c


Or, Factorization of 4a2b4c = 22 × a2 × b4 × c


Factorization of 12a3bc5 = 2 × 2 × 3 × a × a × a × b × c × c × c × c × c


Or, Factorization of 12a3bc5 = 22 × 3 × a3 × b × c5


Factorization of 18a2b3c2 = 2 × 3 × 3 × a × a × b × b × b × c × c


Or, Factorization of 18a2b3c2 = 2 × 32 × a2 × b3 × c2


Now, we need to find the factor of highest power.


Factors of 4a2b4c = 22, a2, b4, c


Factors of 12a3bc5 = 22, 3, a3, b, c5


Factors of 18a2b3c2 = 2, 32, a2, b3, c2


The factors are 22, 32, a3, b4 and c5.


By multiplying these factors, we get


22 × 32 × a3 × b4 × c5 = 4 × 9 a3b4c5


22 × 32 × a3 × b4 × c5 = 36 a3b4c5


Thus, lcm of 4a2b4c, 12a3bc5 and 18a2b3c2 is 36 a3b4c5.


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