What is the Least Common Multiple of 42585 and 42600?

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 42585 and 42600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42585 and 42600, than apply into the LCM equation.

GCF(42585,42600) = 15
LCM(42585,42600) = ( 42585 × 42600) / 15
LCM(42585,42600) = 1814121000 / 15
LCM(42585,42600) = 120941400

Least Common Multiple (LCM) of 42585 and 42600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42585 and 42600. First we will calculate the prime factors of 42585 and 42600.

Prime Factorization of 42585

Prime Factorization of 42600

Now multiplying the highest exponent prime factors to calculate the LCM of 42585 and 42600.

LCM(42585,42600) = 3¹ × 5² × 17¹ × 167¹ × 2³ × 71¹
LCM(42585,42600) = 120941400