What is the Least Common Multiple of 61920 and 61938?

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 61920 and 61938 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 61920 and 61938, than apply into the LCM equation.

GCF(61920,61938) = 18
LCM(61920,61938) = ( 61920 × 61938) / 18
LCM(61920,61938) = 3835200960 / 18
LCM(61920,61938) = 213066720

Least Common Multiple (LCM) of 61920 and 61938 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 61920 and 61938. First we will calculate the prime factors of 61920 and 61938.

Prime Factorization of 61920

Prime Factorization of 61938

Now multiplying the highest exponent prime factors to calculate the LCM of 61920 and 61938.

LCM(61920,61938) = 2⁵ × 3³ × 5¹ × 43¹ × 31¹ × 37¹
LCM(61920,61938) = 213066720