What is the Least Common Multiple of 39696 and 39700?

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 39696 and 39700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39696 and 39700, than apply into the LCM equation.

GCF(39696,39700) = 4
LCM(39696,39700) = ( 39696 × 39700) / 4
LCM(39696,39700) = 1575931200 / 4
LCM(39696,39700) = 393982800

Least Common Multiple (LCM) of 39696 and 39700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39696 and 39700. First we will calculate the prime factors of 39696 and 39700.

Prime Factorization of 39696

Prime Factorization of 39700

Now multiplying the highest exponent prime factors to calculate the LCM of 39696 and 39700.

LCM(39696,39700) = 2⁴ × 3¹ × 827¹ × 5² × 397¹
LCM(39696,39700) = 393982800