Question

Find the LCM of the following set of the numbers by the prime factorisation method.
216, 108, 36 ​

Answer 1

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Answer 2

→ We are given three numbers and asked to find their lowest common multiple by using the method of prime factorization.

Well, a number that is divisible only by 1 and itself is a prime number. So when we say "prime factorization" we mean to write a given number as the product of prime numbers.

→ Enough lecture, let's now find the LCM of the numbers 216, 108 and 36 by the prime factorization method.

$\Large{ \begin{array}{c|c} \tt 2 & \sf{ 216 , 108 , 36} \\ \cline{1-2} \tt 2 & \sf { 108 , 54 , 18} \\ \cline{1-2} \tt 2 & \sf{ 54 , 27 , 9} \\ \cline{1-2} \tt 3 & \sf{ 27 , 27 , 9} \\ \cline{1-2} \tt 3 & \sf{ 9 , 9 , 3 }\\ \cline{1-2} \tt 3 & \sf{ 3 , 3 , 1 }\\ \cline{1-2} & \sf{ 1 , 1 , 1} \end{array}}$

LCM of 216, 108, 36 = 2 x 2 x 2 x 3 x 3 x 3

= 8 x 27

= 216

Therefore, the LCM of 216, 108 and 36 is the number 216 itself.

If the working is not making sense, check the attachment :)