What is the Least Common Multiple of 9585 and 9597?

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 9585 and 9597 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9585 and 9597, than apply into the LCM equation.

GCF(9585,9597) = 3
LCM(9585,9597) = ( 9585 × 9597) / 3
LCM(9585,9597) = 91987245 / 3
LCM(9585,9597) = 30662415

Least Common Multiple (LCM) of 9585 and 9597 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9585 and 9597. First we will calculate the prime factors of 9585 and 9597.

Prime Factorization of 9585

Prime Factorization of 9597

Now multiplying the highest exponent prime factors to calculate the LCM of 9585 and 9597.

LCM(9585,9597) = 3³ × 5¹ × 71¹ × 7¹ × 457¹
LCM(9585,9597) = 30662415