What is the Least Common Multiple of 21564 and 21584?

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 21564 and 21584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21564 and 21584, than apply into the LCM equation.

GCF(21564,21584) = 4
LCM(21564,21584) = ( 21564 × 21584) / 4
LCM(21564,21584) = 465437376 / 4
LCM(21564,21584) = 116359344

Least Common Multiple (LCM) of 21564 and 21584 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21564 and 21584. First we will calculate the prime factors of 21564 and 21584.

Prime Factorization of 21564

Prime Factorization of 21584

Now multiplying the highest exponent prime factors to calculate the LCM of 21564 and 21584.

LCM(21564,21584) = 2⁴ × 3² × 599¹ × 19¹ × 71¹
LCM(21564,21584) = 116359344