What is the Least Common Multiple of 31800 and 31808?

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 31800 and 31808 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31800 and 31808, than apply into the LCM equation.

GCF(31800,31808) = 8
LCM(31800,31808) = ( 31800 × 31808) / 8
LCM(31800,31808) = 1011494400 / 8
LCM(31800,31808) = 126436800

Least Common Multiple (LCM) of 31800 and 31808 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31800 and 31808. First we will calculate the prime factors of 31800 and 31808.

Prime Factorization of 31800

Prime Factorization of 31808

Now multiplying the highest exponent prime factors to calculate the LCM of 31800 and 31808.

LCM(31800,31808) = 2⁶ × 3¹ × 5² × 53¹ × 7¹ × 71¹
LCM(31800,31808) = 126436800