What is the Least Common Multiple of 89700 and 89712?

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 89700 and 89712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 89700 and 89712, than apply into the LCM equation.

GCF(89700,89712) = 12
LCM(89700,89712) = ( 89700 × 89712) / 12
LCM(89700,89712) = 8047166400 / 12
LCM(89700,89712) = 670597200

Least Common Multiple (LCM) of 89700 and 89712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 89700 and 89712. First we will calculate the prime factors of 89700 and 89712.

Prime Factorization of 89700

Prime Factorization of 89712

Now multiplying the highest exponent prime factors to calculate the LCM of 89700 and 89712.

LCM(89700,89712) = 2⁴ × 3² × 5² × 13¹ × 23¹ × 7¹ × 89¹
LCM(89700,89712) = 670597200