What is the Least Common Multiple of 31425 and 31440?

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 31425 and 31440 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31425 and 31440, than apply into the LCM equation.

GCF(31425,31440) = 15
LCM(31425,31440) = ( 31425 × 31440) / 15
LCM(31425,31440) = 988002000 / 15
LCM(31425,31440) = 65866800

Least Common Multiple (LCM) of 31425 and 31440 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31425 and 31440. First we will calculate the prime factors of 31425 and 31440.

Prime Factorization of 31425

Prime Factorization of 31440

Now multiplying the highest exponent prime factors to calculate the LCM of 31425 and 31440.

LCM(31425,31440) = 3¹ × 5² × 419¹ × 2⁴ × 131¹
LCM(31425,31440) = 65866800