What is the Least Common Multiple of 42360 and 42378?

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 42360 and 42378 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42360 and 42378, than apply into the LCM equation.

GCF(42360,42378) = 6
LCM(42360,42378) = ( 42360 × 42378) / 6
LCM(42360,42378) = 1795132080 / 6
LCM(42360,42378) = 299188680

Least Common Multiple (LCM) of 42360 and 42378 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42360 and 42378. First we will calculate the prime factors of 42360 and 42378.

Prime Factorization of 42360

Prime Factorization of 42378

Now multiplying the highest exponent prime factors to calculate the LCM of 42360 and 42378.

LCM(42360,42378) = 2³ × 3¹ × 5¹ × 353¹ × 7¹ × 1009¹
LCM(42360,42378) = 299188680