What is the Least Common Multiple of 4125 and 4140?

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 4125 and 4140 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4125 and 4140, than apply into the LCM equation.

GCF(4125,4140) = 15
LCM(4125,4140) = ( 4125 × 4140) / 15
LCM(4125,4140) = 17077500 / 15
LCM(4125,4140) = 1138500

Least Common Multiple (LCM) of 4125 and 4140 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 4125 and 4140. First we will calculate the prime factors of 4125 and 4140.

Prime Factorization of 4125

Prime Factorization of 4140

Now multiplying the highest exponent prime factors to calculate the LCM of 4125 and 4140.

LCM(4125,4140) = 3² × 5³ × 11¹ × 2² × 23¹
LCM(4125,4140) = 1138500