What is the Least Common Multiple of 21084 and 21096?

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 21084 and 21096 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21084 and 21096, than apply into the LCM equation.

GCF(21084,21096) = 12
LCM(21084,21096) = ( 21084 × 21096) / 12
LCM(21084,21096) = 444788064 / 12
LCM(21084,21096) = 37065672

Least Common Multiple (LCM) of 21084 and 21096 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21084 and 21096. First we will calculate the prime factors of 21084 and 21096.

Prime Factorization of 21084

Prime Factorization of 21096

Now multiplying the highest exponent prime factors to calculate the LCM of 21084 and 21096.

LCM(21084,21096) = 2³ × 3² × 7¹ × 251¹ × 293¹
LCM(21084,21096) = 37065672