What is the Least Common Multiple of 21645 and 21660?

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 21645 and 21660 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21645 and 21660, than apply into the LCM equation.

GCF(21645,21660) = 15
LCM(21645,21660) = ( 21645 × 21660) / 15
LCM(21645,21660) = 468830700 / 15
LCM(21645,21660) = 31255380

Least Common Multiple (LCM) of 21645 and 21660 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21645 and 21660. First we will calculate the prime factors of 21645 and 21660.

Prime Factorization of 21645

Prime Factorization of 21660

Now multiplying the highest exponent prime factors to calculate the LCM of 21645 and 21660.

LCM(21645,21660) = 3² × 5¹ × 13¹ × 37¹ × 2² × 19²
LCM(21645,21660) = 31255380