What is the Least Common Multiple of 30720 and 30738?

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 30720 and 30738 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30720 and 30738, than apply into the LCM equation.

GCF(30720,30738) = 6
LCM(30720,30738) = ( 30720 × 30738) / 6
LCM(30720,30738) = 944271360 / 6
LCM(30720,30738) = 157378560

Least Common Multiple (LCM) of 30720 and 30738 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30720 and 30738. First we will calculate the prime factors of 30720 and 30738.

Prime Factorization of 30720

Prime Factorization of 30738

Now multiplying the highest exponent prime factors to calculate the LCM of 30720 and 30738.

LCM(30720,30738) = 2¹¹ × 3¹ × 5¹ × 47¹ × 109¹
LCM(30720,30738) = 157378560