What is the Least Common Multiple of 31410 and 31414?

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 31410 and 31414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31410 and 31414, than apply into the LCM equation.

GCF(31410,31414) = 2
LCM(31410,31414) = ( 31410 × 31414) / 2
LCM(31410,31414) = 986713740 / 2
LCM(31410,31414) = 493356870

Least Common Multiple (LCM) of 31410 and 31414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31410 and 31414. First we will calculate the prime factors of 31410 and 31414.

Prime Factorization of 31410

Prime Factorization of 31414

Now multiplying the highest exponent prime factors to calculate the LCM of 31410 and 31414.

LCM(31410,31414) = 2¹ × 3² × 5¹ × 349¹ × 113¹ × 139¹
LCM(31410,31414) = 493356870