What is the Least Common Multiple of 31140 and 31149?

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 31140 and 31149 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31140 and 31149, than apply into the LCM equation.

GCF(31140,31149) = 9
LCM(31140,31149) = ( 31140 × 31149) / 9
LCM(31140,31149) = 969979860 / 9
LCM(31140,31149) = 107775540

Least Common Multiple (LCM) of 31140 and 31149 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31140 and 31149. First we will calculate the prime factors of 31140 and 31149.

Prime Factorization of 31140

Prime Factorization of 31149

Now multiplying the highest exponent prime factors to calculate the LCM of 31140 and 31149.

LCM(31140,31149) = 2² × 3² × 5¹ × 173¹ × 3461¹
LCM(31140,31149) = 107775540