What is the Least Common Multiple of 30072 and 30080?

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 30072 and 30080 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30072 and 30080, than apply into the LCM equation.

GCF(30072,30080) = 8
LCM(30072,30080) = ( 30072 × 30080) / 8
LCM(30072,30080) = 904565760 / 8
LCM(30072,30080) = 113070720

Least Common Multiple (LCM) of 30072 and 30080 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30072 and 30080. First we will calculate the prime factors of 30072 and 30080.

Prime Factorization of 30072

Prime Factorization of 30080

Now multiplying the highest exponent prime factors to calculate the LCM of 30072 and 30080.

LCM(30072,30080) = 2⁷ × 3¹ × 7¹ × 179¹ × 5¹ × 47¹
LCM(30072,30080) = 113070720