What is the Least Common Multiple of 21684 and 21689?

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 21689 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 21689, than apply into the LCM equation.

GCF(21684,21689) = 1
LCM(21684,21689) = ( 21684 × 21689) / 1
LCM(21684,21689) = 470304276 / 1
LCM(21684,21689) = 470304276

Least Common Multiple (LCM) of 21684 and 21689 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21684 and 21689. First we will calculate the prime factors of 21684 and 21689.

Prime Factorization of 21684

Prime Factorization of 21689

Now multiplying the highest exponent prime factors to calculate the LCM of 21684 and 21689.

LCM(21684,21689) = 2² × 3¹ × 13¹ × 139¹ × 23² × 41¹
LCM(21684,21689) = 470304276