What is the Least Common Multiple of 39720 and 39728?

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 39720 and 39728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39720 and 39728, than apply into the LCM equation.

GCF(39720,39728) = 8
LCM(39720,39728) = ( 39720 × 39728) / 8
LCM(39720,39728) = 1577996160 / 8
LCM(39720,39728) = 197249520

Least Common Multiple (LCM) of 39720 and 39728 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39720 and 39728. First we will calculate the prime factors of 39720 and 39728.

Prime Factorization of 39720

Prime Factorization of 39728

Now multiplying the highest exponent prime factors to calculate the LCM of 39720 and 39728.

LCM(39720,39728) = 2⁴ × 3¹ × 5¹ × 331¹ × 13¹ × 191¹
LCM(39720,39728) = 197249520