What is the Least Common Multiple of 75360 and 75380?

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 75360 and 75380 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75360 and 75380, than apply into the LCM equation.

GCF(75360,75380) = 20
LCM(75360,75380) = ( 75360 × 75380) / 20
LCM(75360,75380) = 5680636800 / 20
LCM(75360,75380) = 284031840

Least Common Multiple (LCM) of 75360 and 75380 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75360 and 75380. First we will calculate the prime factors of 75360 and 75380.

Prime Factorization of 75360

Prime Factorization of 75380

Now multiplying the highest exponent prime factors to calculate the LCM of 75360 and 75380.

LCM(75360,75380) = 2⁵ × 3¹ × 5¹ × 157¹ × 3769¹
LCM(75360,75380) = 284031840