What is the Least Common Multiple of 31140 and 31152?

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 31152 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 31152, than apply into the LCM equation.

GCF(31140,31152) = 12
LCM(31140,31152) = ( 31140 × 31152) / 12
LCM(31140,31152) = 970073280 / 12
LCM(31140,31152) = 80839440

Least Common Multiple (LCM) of 31140 and 31152 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31140 and 31152. First we will calculate the prime factors of 31140 and 31152.

Prime Factorization of 31140

Prime Factorization of 31152

Now multiplying the highest exponent prime factors to calculate the LCM of 31140 and 31152.

LCM(31140,31152) = 2⁴ × 3² × 5¹ × 173¹ × 11¹ × 59¹
LCM(31140,31152) = 80839440