What is the Least Common Multiple of 31356 and 31374?

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 31356 and 31374 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31356 and 31374, than apply into the LCM equation.

GCF(31356,31374) = 18
LCM(31356,31374) = ( 31356 × 31374) / 18
LCM(31356,31374) = 983763144 / 18
LCM(31356,31374) = 54653508

Least Common Multiple (LCM) of 31356 and 31374 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31356 and 31374. First we will calculate the prime factors of 31356 and 31374.

Prime Factorization of 31356

Prime Factorization of 31374

Now multiplying the highest exponent prime factors to calculate the LCM of 31356 and 31374.

LCM(31356,31374) = 2² × 3³ × 13¹ × 67¹ × 7¹ × 83¹
LCM(31356,31374) = 54653508