What is the Least Common Multiple of 5025 and 5040?

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 5025 and 5040 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5025 and 5040, than apply into the LCM equation.

GCF(5025,5040) = 15
LCM(5025,5040) = ( 5025 × 5040) / 15
LCM(5025,5040) = 25326000 / 15
LCM(5025,5040) = 1688400

Least Common Multiple (LCM) of 5025 and 5040 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5025 and 5040. First we will calculate the prime factors of 5025 and 5040.

Prime Factorization of 5025

Prime Factorization of 5040

Now multiplying the highest exponent prime factors to calculate the LCM of 5025 and 5040.

LCM(5025,5040) = 3² × 5² × 67¹ × 2⁴ × 7¹
LCM(5025,5040) = 1688400