What is the Least Common Multiple of 42720 and 42738?

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 42720 and 42738 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42720 and 42738, than apply into the LCM equation.

GCF(42720,42738) = 6
LCM(42720,42738) = ( 42720 × 42738) / 6
LCM(42720,42738) = 1825767360 / 6
LCM(42720,42738) = 304294560

Least Common Multiple (LCM) of 42720 and 42738 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42720 and 42738. First we will calculate the prime factors of 42720 and 42738.

Prime Factorization of 42720

Prime Factorization of 42738

Now multiplying the highest exponent prime factors to calculate the LCM of 42720 and 42738.

LCM(42720,42738) = 2⁵ × 3¹ × 5¹ × 89¹ × 17¹ × 419¹
LCM(42720,42738) = 304294560