What is the Least Common Multiple of 31605 and 31614?

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 31605 and 31614 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31605 and 31614, than apply into the LCM equation.

GCF(31605,31614) = 3
LCM(31605,31614) = ( 31605 × 31614) / 3
LCM(31605,31614) = 999160470 / 3
LCM(31605,31614) = 333053490

Least Common Multiple (LCM) of 31605 and 31614 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31605 and 31614. First we will calculate the prime factors of 31605 and 31614.

Prime Factorization of 31605

Prime Factorization of 31614

Now multiplying the highest exponent prime factors to calculate the LCM of 31605 and 31614.

LCM(31605,31614) = 3¹ × 5¹ × 7² × 43¹ × 2¹ × 11¹ × 479¹
LCM(31605,31614) = 333053490