What is the Least Common Multiple of 31712 and 31717?

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 31712 and 31717 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31712 and 31717, than apply into the LCM equation.

GCF(31712,31717) = 1
LCM(31712,31717) = ( 31712 × 31717) / 1
LCM(31712,31717) = 1005809504 / 1
LCM(31712,31717) = 1005809504

Least Common Multiple (LCM) of 31712 and 31717 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31712 and 31717. First we will calculate the prime factors of 31712 and 31717.

Prime Factorization of 31712

Prime Factorization of 31717

Now multiplying the highest exponent prime factors to calculate the LCM of 31712 and 31717.

LCM(31712,31717) = 2⁵ × 991¹ × 7¹ × 23¹ × 197¹
LCM(31712,31717) = 1005809504