What is the Least Common Multiple of 42075 and 42084?

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 42075 and 42084 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42075 and 42084, than apply into the LCM equation.

GCF(42075,42084) = 9
LCM(42075,42084) = ( 42075 × 42084) / 9
LCM(42075,42084) = 1770684300 / 9
LCM(42075,42084) = 196742700

Least Common Multiple (LCM) of 42075 and 42084 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42075 and 42084. First we will calculate the prime factors of 42075 and 42084.

Prime Factorization of 42075

Prime Factorization of 42084

Now multiplying the highest exponent prime factors to calculate the LCM of 42075 and 42084.

LCM(42075,42084) = 3² × 5² × 11¹ × 17¹ × 2² × 7¹ × 167¹
LCM(42075,42084) = 196742700