What is the Least Common Multiple of 89100 and 89120?

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 89100 and 89120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 89100 and 89120, than apply into the LCM equation.

GCF(89100,89120) = 20
LCM(89100,89120) = ( 89100 × 89120) / 20
LCM(89100,89120) = 7940592000 / 20
LCM(89100,89120) = 397029600

Least Common Multiple (LCM) of 89100 and 89120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 89100 and 89120. First we will calculate the prime factors of 89100 and 89120.

Prime Factorization of 89100

Prime Factorization of 89120

Now multiplying the highest exponent prime factors to calculate the LCM of 89100 and 89120.

LCM(89100,89120) = 2⁵ × 3⁴ × 5² × 11¹ × 557¹
LCM(89100,89120) = 397029600