What is the Least Common Multiple of 89400 and 89420?

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 89400 and 89420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 89400 and 89420, than apply into the LCM equation.

GCF(89400,89420) = 20
LCM(89400,89420) = ( 89400 × 89420) / 20
LCM(89400,89420) = 7994148000 / 20
LCM(89400,89420) = 399707400

Least Common Multiple (LCM) of 89400 and 89420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 89400 and 89420. First we will calculate the prime factors of 89400 and 89420.

Prime Factorization of 89400

Prime Factorization of 89420

Now multiplying the highest exponent prime factors to calculate the LCM of 89400 and 89420.

LCM(89400,89420) = 2³ × 3¹ × 5² × 149¹ × 17¹ × 263¹
LCM(89400,89420) = 399707400