What is the Least Common Multiple of 9600 and 9612?

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 9600 and 9612 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9600 and 9612, than apply into the LCM equation.

GCF(9600,9612) = 12
LCM(9600,9612) = ( 9600 × 9612) / 12
LCM(9600,9612) = 92275200 / 12
LCM(9600,9612) = 7689600

Least Common Multiple (LCM) of 9600 and 9612 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9600 and 9612. First we will calculate the prime factors of 9600 and 9612.

Prime Factorization of 9600

Prime Factorization of 9612

Now multiplying the highest exponent prime factors to calculate the LCM of 9600 and 9612.

LCM(9600,9612) = 2⁷ × 3³ × 5² × 89¹
LCM(9600,9612) = 7689600