What is the Least Common Multiple of 90825 and 90840?

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 90825 and 90840 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90825 and 90840, than apply into the LCM equation.

GCF(90825,90840) = 15
LCM(90825,90840) = ( 90825 × 90840) / 15
LCM(90825,90840) = 8250543000 / 15
LCM(90825,90840) = 550036200

Least Common Multiple (LCM) of 90825 and 90840 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90825 and 90840. First we will calculate the prime factors of 90825 and 90840.

Prime Factorization of 90825

Prime Factorization of 90840

Now multiplying the highest exponent prime factors to calculate the LCM of 90825 and 90840.

LCM(90825,90840) = 3¹ × 5² × 7¹ × 173¹ × 2³ × 757¹
LCM(90825,90840) = 550036200