What is the Least Common Multiple of 31705 and 31712?

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 31705 and 31712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31705 and 31712, than apply into the LCM equation.

GCF(31705,31712) = 1
LCM(31705,31712) = ( 31705 × 31712) / 1
LCM(31705,31712) = 1005428960 / 1
LCM(31705,31712) = 1005428960

Least Common Multiple (LCM) of 31705 and 31712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31705 and 31712. First we will calculate the prime factors of 31705 and 31712.

Prime Factorization of 31705

Prime Factorization of 31712

Now multiplying the highest exponent prime factors to calculate the LCM of 31705 and 31712.

LCM(31705,31712) = 5¹ × 17¹ × 373¹ × 2⁵ × 991¹
LCM(31705,31712) = 1005428960