What is the Least Common Multiple of 21684 and 21693?

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 21684 and 21693 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21684 and 21693, than apply into the LCM equation.

GCF(21684,21693) = 3
LCM(21684,21693) = ( 21684 × 21693) / 3
LCM(21684,21693) = 470391012 / 3
LCM(21684,21693) = 156797004

Least Common Multiple (LCM) of 21684 and 21693 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21684 and 21693. First we will calculate the prime factors of 21684 and 21693.

Prime Factorization of 21684

Prime Factorization of 21693

Now multiplying the highest exponent prime factors to calculate the LCM of 21684 and 21693.

LCM(21684,21693) = 2² × 3¹ × 13¹ × 139¹ × 7¹ × 1033¹
LCM(21684,21693) = 156797004