What is the Least Common Multiple of 75120 and 75140?

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 75120 and 75140 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75120 and 75140, than apply into the LCM equation.

GCF(75120,75140) = 20
LCM(75120,75140) = ( 75120 × 75140) / 20
LCM(75120,75140) = 5644516800 / 20
LCM(75120,75140) = 282225840

Least Common Multiple (LCM) of 75120 and 75140 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75120 and 75140. First we will calculate the prime factors of 75120 and 75140.

Prime Factorization of 75120

Prime Factorization of 75140

Now multiplying the highest exponent prime factors to calculate the LCM of 75120 and 75140.

LCM(75120,75140) = 2⁴ × 3¹ × 5¹ × 313¹ × 13¹ × 17²
LCM(75120,75140) = 282225840