What is the Least Common Multiple of 21585 and 21596?

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 21585 and 21596 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21585 and 21596, than apply into the LCM equation.

GCF(21585,21596) = 1
LCM(21585,21596) = ( 21585 × 21596) / 1
LCM(21585,21596) = 466149660 / 1
LCM(21585,21596) = 466149660

Least Common Multiple (LCM) of 21585 and 21596 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21585 and 21596. First we will calculate the prime factors of 21585 and 21596.

Prime Factorization of 21585

Prime Factorization of 21596

Now multiplying the highest exponent prime factors to calculate the LCM of 21585 and 21596.

LCM(21585,21596) = 3¹ × 5¹ × 1439¹ × 2² × 5399¹
LCM(21585,21596) = 466149660