What is the Least Common Multiple of 42960 and 42975?

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 42960 and 42975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42960 and 42975, than apply into the LCM equation.

GCF(42960,42975) = 15
LCM(42960,42975) = ( 42960 × 42975) / 15
LCM(42960,42975) = 1846206000 / 15
LCM(42960,42975) = 123080400

Least Common Multiple (LCM) of 42960 and 42975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42960 and 42975. First we will calculate the prime factors of 42960 and 42975.

Prime Factorization of 42960

Prime Factorization of 42975

Now multiplying the highest exponent prime factors to calculate the LCM of 42960 and 42975.

LCM(42960,42975) = 2⁴ × 3² × 5² × 179¹ × 191¹
LCM(42960,42975) = 123080400