What is the Least Common Multiple of 21120 and 21125?

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 21120 and 21125 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21120 and 21125, than apply into the LCM equation.

GCF(21120,21125) = 5
LCM(21120,21125) = ( 21120 × 21125) / 5
LCM(21120,21125) = 446160000 / 5
LCM(21120,21125) = 89232000

Least Common Multiple (LCM) of 21120 and 21125 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21120 and 21125. First we will calculate the prime factors of 21120 and 21125.

Prime Factorization of 21120

Prime Factorization of 21125

Now multiplying the highest exponent prime factors to calculate the LCM of 21120 and 21125.

LCM(21120,21125) = 2⁷ × 3¹ × 5³ × 11¹ × 13²
LCM(21120,21125) = 89232000