What is the Least Common Multiple of 31654 and 31674?

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 31654 and 31674 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31654 and 31674, than apply into the LCM equation.

GCF(31654,31674) = 2
LCM(31654,31674) = ( 31654 × 31674) / 2
LCM(31654,31674) = 1002608796 / 2
LCM(31654,31674) = 501304398

Least Common Multiple (LCM) of 31654 and 31674 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31654 and 31674. First we will calculate the prime factors of 31654 and 31674.

Prime Factorization of 31654

Prime Factorization of 31674

Now multiplying the highest exponent prime factors to calculate the LCM of 31654 and 31674.

LCM(31654,31674) = 2¹ × 7² × 17¹ × 19¹ × 3¹ × 5279¹
LCM(31654,31674) = 501304398