What is the Least Common Multiple of 90384 and 90396?

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 90384 and 90396 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90384 and 90396, than apply into the LCM equation.

GCF(90384,90396) = 12
LCM(90384,90396) = ( 90384 × 90396) / 12
LCM(90384,90396) = 8170352064 / 12
LCM(90384,90396) = 680862672

Least Common Multiple (LCM) of 90384 and 90396 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90384 and 90396. First we will calculate the prime factors of 90384 and 90396.

Prime Factorization of 90384

Prime Factorization of 90396

Now multiplying the highest exponent prime factors to calculate the LCM of 90384 and 90396.

LCM(90384,90396) = 2⁴ × 3⁶ × 7¹ × 269¹ × 31¹
LCM(90384,90396) = 680862672