What is the Least Common Multiple of 90144 and 90159?

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 90144 and 90159 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90144 and 90159, than apply into the LCM equation.

GCF(90144,90159) = 3
LCM(90144,90159) = ( 90144 × 90159) / 3
LCM(90144,90159) = 8127292896 / 3
LCM(90144,90159) = 2709097632

Least Common Multiple (LCM) of 90144 and 90159 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90144 and 90159. First we will calculate the prime factors of 90144 and 90159.

Prime Factorization of 90144

Prime Factorization of 90159

Now multiplying the highest exponent prime factors to calculate the LCM of 90144 and 90159.

LCM(90144,90159) = 2⁵ × 3² × 313¹ × 41¹ × 733¹
LCM(90144,90159) = 2709097632