What is the Least Common Multiple of 31824 and 31838?

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 31824 and 31838 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31824 and 31838, than apply into the LCM equation.

GCF(31824,31838) = 2
LCM(31824,31838) = ( 31824 × 31838) / 2
LCM(31824,31838) = 1013212512 / 2
LCM(31824,31838) = 506606256

Least Common Multiple (LCM) of 31824 and 31838 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31824 and 31838. First we will calculate the prime factors of 31824 and 31838.

Prime Factorization of 31824

Prime Factorization of 31838

Now multiplying the highest exponent prime factors to calculate the LCM of 31824 and 31838.

LCM(31824,31838) = 2⁴ × 3² × 13¹ × 17¹ × 15919¹
LCM(31824,31838) = 506606256