What is the Least Common Multiple of 21570 and 21585?

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 21570 and 21585 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21570 and 21585, than apply into the LCM equation.

GCF(21570,21585) = 15
LCM(21570,21585) = ( 21570 × 21585) / 15
LCM(21570,21585) = 465588450 / 15
LCM(21570,21585) = 31039230

Least Common Multiple (LCM) of 21570 and 21585 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21570 and 21585. First we will calculate the prime factors of 21570 and 21585.

Prime Factorization of 21570

Prime Factorization of 21585

Now multiplying the highest exponent prime factors to calculate the LCM of 21570 and 21585.

LCM(21570,21585) = 2¹ × 3¹ × 5¹ × 719¹ × 1439¹
LCM(21570,21585) = 31039230