What is the Least Common Multiple of 17712 and 17719?

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 17712 and 17719 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17712 and 17719, than apply into the LCM equation.

GCF(17712,17719) = 1
LCM(17712,17719) = ( 17712 × 17719) / 1
LCM(17712,17719) = 313838928 / 1
LCM(17712,17719) = 313838928

Least Common Multiple (LCM) of 17712 and 17719 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17712 and 17719. First we will calculate the prime factors of 17712 and 17719.

Prime Factorization of 17712

Prime Factorization of 17719

Now multiplying the highest exponent prime factors to calculate the LCM of 17712 and 17719.

LCM(17712,17719) = 2⁴ × 3³ × 41¹ × 13¹ × 29¹ × 47¹
LCM(17712,17719) = 313838928