What is the Least Common Multiple of 31974 and 31984?

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 31974 and 31984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31974 and 31984, than apply into the LCM equation.

GCF(31974,31984) = 2
LCM(31974,31984) = ( 31974 × 31984) / 2
LCM(31974,31984) = 1022656416 / 2
LCM(31974,31984) = 511328208

Least Common Multiple (LCM) of 31974 and 31984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31974 and 31984. First we will calculate the prime factors of 31974 and 31984.

Prime Factorization of 31974

Prime Factorization of 31984

Now multiplying the highest exponent prime factors to calculate the LCM of 31974 and 31984.

LCM(31974,31984) = 2⁴ × 3¹ × 73² × 1999¹
LCM(31974,31984) = 511328208