What is the Least Common Multiple of 31734 and 31744?

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 31744 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 31744, than apply into the LCM equation.

GCF(31734,31744) = 2
LCM(31734,31744) = ( 31734 × 31744) / 2
LCM(31734,31744) = 1007364096 / 2
LCM(31734,31744) = 503682048

Least Common Multiple (LCM) of 31734 and 31744 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31734 and 31744. First we will calculate the prime factors of 31734 and 31744.

Prime Factorization of 31734

Prime Factorization of 31744

Now multiplying the highest exponent prime factors to calculate the LCM of 31734 and 31744.

LCM(31734,31744) = 2¹⁰ × 3² × 41¹ × 43¹ × 31¹
LCM(31734,31744) = 503682048