What is the Least Common Multiple of 9576 and 9585?

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 9576 and 9585 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9576 and 9585, than apply into the LCM equation.

GCF(9576,9585) = 9
LCM(9576,9585) = ( 9576 × 9585) / 9
LCM(9576,9585) = 91785960 / 9
LCM(9576,9585) = 10198440

Least Common Multiple (LCM) of 9576 and 9585 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9576 and 9585. First we will calculate the prime factors of 9576 and 9585.

Prime Factorization of 9576

Prime Factorization of 9585

Now multiplying the highest exponent prime factors to calculate the LCM of 9576 and 9585.

LCM(9576,9585) = 2³ × 3³ × 7¹ × 19¹ × 5¹ × 71¹
LCM(9576,9585) = 10198440