What is the Least Common Multiple of 31794 and 31800?

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 31794 and 31800 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31794 and 31800, than apply into the LCM equation.

GCF(31794,31800) = 6
LCM(31794,31800) = ( 31794 × 31800) / 6
LCM(31794,31800) = 1011049200 / 6
LCM(31794,31800) = 168508200

Least Common Multiple (LCM) of 31794 and 31800 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31794 and 31800. First we will calculate the prime factors of 31794 and 31800.

Prime Factorization of 31794

Prime Factorization of 31800

Now multiplying the highest exponent prime factors to calculate the LCM of 31794 and 31800.

LCM(31794,31800) = 2³ × 3¹ × 7¹ × 757¹ × 5² × 53¹
LCM(31794,31800) = 168508200