What is the Least Common Multiple of 9675 and 9680?

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 9675 and 9680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9675 and 9680, than apply into the LCM equation.

GCF(9675,9680) = 5
LCM(9675,9680) = ( 9675 × 9680) / 5
LCM(9675,9680) = 93654000 / 5
LCM(9675,9680) = 18730800

Least Common Multiple (LCM) of 9675 and 9680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9675 and 9680. First we will calculate the prime factors of 9675 and 9680.

Prime Factorization of 9675

Prime Factorization of 9680

Now multiplying the highest exponent prime factors to calculate the LCM of 9675 and 9680.

LCM(9675,9680) = 3² × 5² × 43¹ × 2⁴ × 11²
LCM(9675,9680) = 18730800