What is the Least Common Multiple of 31734 and 31740?

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 31734 and 31740 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31734 and 31740, than apply into the LCM equation.

GCF(31734,31740) = 6
LCM(31734,31740) = ( 31734 × 31740) / 6
LCM(31734,31740) = 1007237160 / 6
LCM(31734,31740) = 167872860

Least Common Multiple (LCM) of 31734 and 31740 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31734 and 31740. First we will calculate the prime factors of 31734 and 31740.

Prime Factorization of 31734

Prime Factorization of 31740

Now multiplying the highest exponent prime factors to calculate the LCM of 31734 and 31740.

LCM(31734,31740) = 2² × 3² × 41¹ × 43¹ × 5¹ × 23²
LCM(31734,31740) = 167872860