What is the Least Common Multiple of 75100 and 75120?

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 75100 and 75120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75100 and 75120, than apply into the LCM equation.

GCF(75100,75120) = 20
LCM(75100,75120) = ( 75100 × 75120) / 20
LCM(75100,75120) = 5641512000 / 20
LCM(75100,75120) = 282075600

Least Common Multiple (LCM) of 75100 and 75120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75100 and 75120. First we will calculate the prime factors of 75100 and 75120.

Prime Factorization of 75100

Prime Factorization of 75120

Now multiplying the highest exponent prime factors to calculate the LCM of 75100 and 75120.

LCM(75100,75120) = 2⁴ × 5² × 751¹ × 3¹ × 313¹
LCM(75100,75120) = 282075600