What is the Least Common Multiple of 75030 and 75040?

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 75030 and 75040 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75030 and 75040, than apply into the LCM equation.

GCF(75030,75040) = 10
LCM(75030,75040) = ( 75030 × 75040) / 10
LCM(75030,75040) = 5630251200 / 10
LCM(75030,75040) = 563025120

Least Common Multiple (LCM) of 75030 and 75040 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75030 and 75040. First we will calculate the prime factors of 75030 and 75040.

Prime Factorization of 75030

Prime Factorization of 75040

Now multiplying the highest exponent prime factors to calculate the LCM of 75030 and 75040.

LCM(75030,75040) = 2⁵ × 3¹ × 5¹ × 41¹ × 61¹ × 7¹ × 67¹
LCM(75030,75040) = 563025120