What is the Least Common Multiple of 21600 and 21615?

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 21600 and 21615 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21600 and 21615, than apply into the LCM equation.

GCF(21600,21615) = 15
LCM(21600,21615) = ( 21600 × 21615) / 15
LCM(21600,21615) = 466884000 / 15
LCM(21600,21615) = 31125600

Least Common Multiple (LCM) of 21600 and 21615 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21600 and 21615. First we will calculate the prime factors of 21600 and 21615.

Prime Factorization of 21600

Prime Factorization of 21615

Now multiplying the highest exponent prime factors to calculate the LCM of 21600 and 21615.

LCM(21600,21615) = 2⁵ × 3³ × 5² × 11¹ × 131¹
LCM(21600,21615) = 31125600