What is the Least Common Multiple of 90396 and 90400?

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 90396 and 90400 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90396 and 90400, than apply into the LCM equation.

GCF(90396,90400) = 4
LCM(90396,90400) = ( 90396 × 90400) / 4
LCM(90396,90400) = 8171798400 / 4
LCM(90396,90400) = 2042949600

Least Common Multiple (LCM) of 90396 and 90400 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90396 and 90400. First we will calculate the prime factors of 90396 and 90400.

Prime Factorization of 90396

Prime Factorization of 90400

Now multiplying the highest exponent prime factors to calculate the LCM of 90396 and 90400.

LCM(90396,90400) = 2⁵ × 3⁶ × 31¹ × 5² × 113¹
LCM(90396,90400) = 2042949600