What is the Least Common Multiple of 30080 and 30085?

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 30080 and 30085 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30080 and 30085, than apply into the LCM equation.

GCF(30080,30085) = 5
LCM(30080,30085) = ( 30080 × 30085) / 5
LCM(30080,30085) = 904956800 / 5
LCM(30080,30085) = 180991360

Least Common Multiple (LCM) of 30080 and 30085 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30080 and 30085. First we will calculate the prime factors of 30080 and 30085.

Prime Factorization of 30080

Prime Factorization of 30085

Now multiplying the highest exponent prime factors to calculate the LCM of 30080 and 30085.

LCM(30080,30085) = 2⁷ × 5¹ × 47¹ × 11¹ × 547¹
LCM(30080,30085) = 180991360