What is the Least Common Multiple of 21735 and 21744?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 21735 and 21744 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21735 and 21744, than apply into the LCM equation.

GCF(21735,21744) = 9
LCM(21735,21744) = ( 21735 × 21744) / 9
LCM(21735,21744) = 472605840 / 9
LCM(21735,21744) = 52511760

Least Common Multiple (LCM) of 21735 and 21744 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21735 and 21744. First we will calculate the prime factors of 21735 and 21744.

Prime Factorization of 21735

Prime Factorization of 21744

Now multiplying the highest exponent prime factors to calculate the LCM of 21735 and 21744.

LCM(21735,21744) = 3³ × 5¹ × 7¹ × 23¹ × 2⁴ × 151¹
LCM(21735,21744) = 52511760