Question

Find the least common multiple of 12,15 and 18?

Answer 1

Hint: To determine the LCM of a given number, first discover the multiples of each individual number, then we will find the product of common factors in all three, common in either 2 and then the remaining number.

Complete step by step answer:
We have to find the L.C.M. of 12,15 and 18.
We will first consider the factors of each number.
Factors of 12 is
$ \Rightarrow 12 = 2 \times 2 \times 3$
Factors of 15 is
$ \Rightarrow 15 = 3 \times 5$
And, the factors of 18 is
$ \Rightarrow 18 = 2 \times 3 \times 3$
We will find the product of common factors in all three, common in either 2 and then the remaining number.
So, we have one 3 is common in 12,15 and 18, one 2 is common in 12 and 18 and one 2, one 3 and one 5 is remaining in all three.
The L.C.M. of 12, 15 and 18
$ \Rightarrow L.C.M = 3 \times 2 \times 2 \times 3 \times 5$
$ \Rightarrow L.C.M = 180$
Hence, The L.C.M. of 12, 15 and 18 is 180.

Note:
We can also find the L.C.M. using the greatest divisor method, using prime factorization or by using continuous division method. We have used the factorization method in the above question. We can also find the H.C.F of the number at the same time if we are using the factorization method just by one taking the product of the factors which are common in any two of the numbers.