What is the Least Common Multiple of 21096 and 21105?

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 21096 and 21105 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21096 and 21105, than apply into the LCM equation.

GCF(21096,21105) = 9
LCM(21096,21105) = ( 21096 × 21105) / 9
LCM(21096,21105) = 445231080 / 9
LCM(21096,21105) = 49470120

Least Common Multiple (LCM) of 21096 and 21105 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21096 and 21105. First we will calculate the prime factors of 21096 and 21105.

Prime Factorization of 21096

Prime Factorization of 21105

Now multiplying the highest exponent prime factors to calculate the LCM of 21096 and 21105.

LCM(21096,21105) = 2³ × 3² × 293¹ × 5¹ × 7¹ × 67¹
LCM(21096,21105) = 49470120