What is the Least Common Multiple of 10464 and 10470?

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 10464 and 10470 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10464 and 10470, than apply into the LCM equation.

GCF(10464,10470) = 6
LCM(10464,10470) = ( 10464 × 10470) / 6
LCM(10464,10470) = 109558080 / 6
LCM(10464,10470) = 18259680

Least Common Multiple (LCM) of 10464 and 10470 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10464 and 10470. First we will calculate the prime factors of 10464 and 10470.

Prime Factorization of 10464

Prime Factorization of 10470

Now multiplying the highest exponent prime factors to calculate the LCM of 10464 and 10470.

LCM(10464,10470) = 2⁵ × 3¹ × 109¹ × 5¹ × 349¹
LCM(10464,10470) = 18259680