What is the Least Common Multiple of 78720 and 78740?

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 78720 and 78740 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78720 and 78740, than apply into the LCM equation.

GCF(78720,78740) = 20
LCM(78720,78740) = ( 78720 × 78740) / 20
LCM(78720,78740) = 6198412800 / 20
LCM(78720,78740) = 309920640

Least Common Multiple (LCM) of 78720 and 78740 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78720 and 78740. First we will calculate the prime factors of 78720 and 78740.

Prime Factorization of 78720

Prime Factorization of 78740

Now multiplying the highest exponent prime factors to calculate the LCM of 78720 and 78740.

LCM(78720,78740) = 2⁷ × 3¹ × 5¹ × 41¹ × 31¹ × 127¹
LCM(78720,78740) = 309920640