What is the Least Common Multiple of 31614 and 31632?

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 31614 and 31632 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31614 and 31632, than apply into the LCM equation.

GCF(31614,31632) = 6
LCM(31614,31632) = ( 31614 × 31632) / 6
LCM(31614,31632) = 1000014048 / 6
LCM(31614,31632) = 166669008

Least Common Multiple (LCM) of 31614 and 31632 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31614 and 31632. First we will calculate the prime factors of 31614 and 31632.

Prime Factorization of 31614

Prime Factorization of 31632

Now multiplying the highest exponent prime factors to calculate the LCM of 31614 and 31632.

LCM(31614,31632) = 2⁴ × 3¹ × 11¹ × 479¹ × 659¹
LCM(31614,31632) = 166669008