What is the Least Common Multiple of 39894 and 39900?

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 39894 and 39900 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39894 and 39900, than apply into the LCM equation.

GCF(39894,39900) = 6
LCM(39894,39900) = ( 39894 × 39900) / 6
LCM(39894,39900) = 1591770600 / 6
LCM(39894,39900) = 265295100

Least Common Multiple (LCM) of 39894 and 39900 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39894 and 39900. First we will calculate the prime factors of 39894 and 39900.

Prime Factorization of 39894

Prime Factorization of 39900

Now multiplying the highest exponent prime factors to calculate the LCM of 39894 and 39900.

LCM(39894,39900) = 2² × 3¹ × 61¹ × 109¹ × 5² × 7¹ × 19¹
LCM(39894,39900) = 265295100