What is the Least Common Multiple of 37920 and 37935?

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 37920 and 37935 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37920 and 37935, than apply into the LCM equation.

GCF(37920,37935) = 15
LCM(37920,37935) = ( 37920 × 37935) / 15
LCM(37920,37935) = 1438495200 / 15
LCM(37920,37935) = 95899680

Least Common Multiple (LCM) of 37920 and 37935 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37920 and 37935. First we will calculate the prime factors of 37920 and 37935.

Prime Factorization of 37920

Prime Factorization of 37935

Now multiplying the highest exponent prime factors to calculate the LCM of 37920 and 37935.

LCM(37920,37935) = 2⁵ × 3³ × 5¹ × 79¹ × 281¹
LCM(37920,37935) = 95899680