What is the Least Common Multiple of 42204 and 42210?

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 42204 and 42210 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42204 and 42210, than apply into the LCM equation.

GCF(42204,42210) = 6
LCM(42204,42210) = ( 42204 × 42210) / 6
LCM(42204,42210) = 1781430840 / 6
LCM(42204,42210) = 296905140

Least Common Multiple (LCM) of 42204 and 42210 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42204 and 42210. First we will calculate the prime factors of 42204 and 42210.

Prime Factorization of 42204

Prime Factorization of 42210

Now multiplying the highest exponent prime factors to calculate the LCM of 42204 and 42210.

LCM(42204,42210) = 2² × 3² × 3517¹ × 5¹ × 7¹ × 67¹
LCM(42204,42210) = 296905140