Question

Find the L.C.M.of $108,135,162$ by prime factorisation method

Answer 1

Prime Fatorization method : In this method , we write the prime factorisation of each of the given numbers.

L.C.M is the product of all the different prime factors of the given numbers using each common prime factor the greatest number of times it appears in the prime factorisation of any of the given numbers .

$$\begin{gathered} 108=2\times 2\times 3\times 3 \\ 135=3\times 3\times 3\times 5 \\ 162=2\times 3\times 3\times 3\times 3 \end{gathered}$$

L.CM. $$\begin{gathered} =2\times 2\times 3\times 3\times 3\times 3\times 5 \\ =1620 \end{gathered}$$. [ Notice that 2 occurs as a prime factor maximum two times , 3 four times , 5 one time. ]

Hence , L.C.M. of $108,135,162$ is $1620$