Question

Find the L.C.M of 24, 36, and 40 by prime factorization.

Hint: In order to find the LCM by prime factorization method first we will factorize each of the given numbers in multiple primes, then by taking a common multiple we will find the LCM.

Given numbers are 24, 36, and 40
First we will find out the factors of each number
Prime multiplication factors for $24 = 2 \times 2 \times 2 \times 3$
Prime multiplication factors for $36 = 2 \times 2 \times 3 \times 3$
Prime multiplication factors for $40 = 2 \times 2 \times 2 \times 5$
We know that
LCM is the product of the greatest power of each prime factor involved in the numbers.
So, the LCM of 24, 36 and 40 is $= 2 \times 2 \times 2 \times 3 \times 3 \times 5 = 360$
Hence, the LCM of 24, 36 and 40 is 360.

Note- The least common multiple, lowest common multiple, or smallest common multiple of two integers “a” and “b”, usually denoted by LCM, is the smallest positive integer that is divisible by both “a” and “b”. Same is the case for the LCM of more than 2 numbers. The LCM is the smallest number which is divisible by all of them.