What is the Least Common Multiple of 37854 and 37872?

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 37854 and 37872 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37854 and 37872, than apply into the LCM equation.

GCF(37854,37872) = 18
LCM(37854,37872) = ( 37854 × 37872) / 18
LCM(37854,37872) = 1433606688 / 18
LCM(37854,37872) = 79644816

Least Common Multiple (LCM) of 37854 and 37872 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37854 and 37872. First we will calculate the prime factors of 37854 and 37872.

Prime Factorization of 37854

Prime Factorization of 37872

Now multiplying the highest exponent prime factors to calculate the LCM of 37854 and 37872.

LCM(37854,37872) = 2⁴ × 3³ × 701¹ × 263¹
LCM(37854,37872) = 79644816