What is the Least Common Multiple of 30360 and 30378?

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 30360 and 30378 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30360 and 30378, than apply into the LCM equation.

GCF(30360,30378) = 6
LCM(30360,30378) = ( 30360 × 30378) / 6
LCM(30360,30378) = 922276080 / 6
LCM(30360,30378) = 153712680

Least Common Multiple (LCM) of 30360 and 30378 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30360 and 30378. First we will calculate the prime factors of 30360 and 30378.

Prime Factorization of 30360

Prime Factorization of 30378

Now multiplying the highest exponent prime factors to calculate the LCM of 30360 and 30378.

LCM(30360,30378) = 2³ × 3¹ × 5¹ × 11¹ × 23¹ × 61¹ × 83¹
LCM(30360,30378) = 153712680