What is the Least Common Multiple of 31992 and 32007?

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 31992 and 32007 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31992 and 32007, than apply into the LCM equation.

GCF(31992,32007) = 3
LCM(31992,32007) = ( 31992 × 32007) / 3
LCM(31992,32007) = 1023967944 / 3
LCM(31992,32007) = 341322648

Least Common Multiple (LCM) of 31992 and 32007 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31992 and 32007. First we will calculate the prime factors of 31992 and 32007.

Prime Factorization of 31992

Prime Factorization of 32007

Now multiplying the highest exponent prime factors to calculate the LCM of 31992 and 32007.

LCM(31992,32007) = 2³ × 3¹ × 31¹ × 43¹ × 47¹ × 227¹
LCM(31992,32007) = 341322648