What is the Least Common Multiple of 7140 and 7149?

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 7140 and 7149 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7140 and 7149, than apply into the LCM equation.

GCF(7140,7149) = 3
LCM(7140,7149) = ( 7140 × 7149) / 3
LCM(7140,7149) = 51043860 / 3
LCM(7140,7149) = 17014620

Least Common Multiple (LCM) of 7140 and 7149 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7140 and 7149. First we will calculate the prime factors of 7140 and 7149.

Prime Factorization of 7140

Prime Factorization of 7149

Now multiplying the highest exponent prime factors to calculate the LCM of 7140 and 7149.

LCM(7140,7149) = 2² × 3¹ × 5¹ × 7¹ × 17¹ × 2383¹
LCM(7140,7149) = 17014620