What is the Least Common Multiple of 31464 and 31470?

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 31464 and 31470 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31464 and 31470, than apply into the LCM equation.

GCF(31464,31470) = 6
LCM(31464,31470) = ( 31464 × 31470) / 6
LCM(31464,31470) = 990172080 / 6
LCM(31464,31470) = 165028680

Least Common Multiple (LCM) of 31464 and 31470 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31464 and 31470. First we will calculate the prime factors of 31464 and 31470.

Prime Factorization of 31464

Prime Factorization of 31470

Now multiplying the highest exponent prime factors to calculate the LCM of 31464 and 31470.

LCM(31464,31470) = 2³ × 3² × 19¹ × 23¹ × 5¹ × 1049¹
LCM(31464,31470) = 165028680