What is the Least Common Multiple of 31665 and 31678?

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 31665 and 31678 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31665 and 31678, than apply into the LCM equation.

GCF(31665,31678) = 1
LCM(31665,31678) = ( 31665 × 31678) / 1
LCM(31665,31678) = 1003083870 / 1
LCM(31665,31678) = 1003083870

Least Common Multiple (LCM) of 31665 and 31678 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31665 and 31678. First we will calculate the prime factors of 31665 and 31678.

Prime Factorization of 31665

Prime Factorization of 31678

Now multiplying the highest exponent prime factors to calculate the LCM of 31665 and 31678.

LCM(31665,31678) = 3¹ × 5¹ × 2111¹ × 2¹ × 47¹ × 337¹
LCM(31665,31678) = 1003083870