What is the Least Common Multiple of 21684 and 21704?

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 21704 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 21704, than apply into the LCM equation.

GCF(21684,21704) = 4
LCM(21684,21704) = ( 21684 × 21704) / 4
LCM(21684,21704) = 470629536 / 4
LCM(21684,21704) = 117657384

Least Common Multiple (LCM) of 21684 and 21704 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21684 and 21704. First we will calculate the prime factors of 21684 and 21704.

Prime Factorization of 21684

Prime Factorization of 21704

Now multiplying the highest exponent prime factors to calculate the LCM of 21684 and 21704.

LCM(21684,21704) = 2³ × 3¹ × 13¹ × 139¹ × 2713¹
LCM(21684,21704) = 117657384