What is the Least Common Multiple of 75420 and 75438?

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 75420 and 75438 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75420 and 75438, than apply into the LCM equation.

GCF(75420,75438) = 18
LCM(75420,75438) = ( 75420 × 75438) / 18
LCM(75420,75438) = 5689533960 / 18
LCM(75420,75438) = 316085220

Least Common Multiple (LCM) of 75420 and 75438 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75420 and 75438. First we will calculate the prime factors of 75420 and 75438.

Prime Factorization of 75420

Prime Factorization of 75438

Now multiplying the highest exponent prime factors to calculate the LCM of 75420 and 75438.

LCM(75420,75438) = 2² × 3³ × 5¹ × 419¹ × 11¹ × 127¹
LCM(75420,75438) = 316085220