What is the Least Common Multiple of 48960 and 48975?

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 48960 and 48975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 48960 and 48975, than apply into the LCM equation.

GCF(48960,48975) = 15
LCM(48960,48975) = ( 48960 × 48975) / 15
LCM(48960,48975) = 2397816000 / 15
LCM(48960,48975) = 159854400

Least Common Multiple (LCM) of 48960 and 48975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 48960 and 48975. First we will calculate the prime factors of 48960 and 48975.

Prime Factorization of 48960

Prime Factorization of 48975

Now multiplying the highest exponent prime factors to calculate the LCM of 48960 and 48975.

LCM(48960,48975) = 2⁶ × 3² × 5² × 17¹ × 653¹
LCM(48960,48975) = 159854400