What is the Least Common Multiple of 13305 and 13312?

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 13305 and 13312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13305 and 13312, than apply into the LCM equation.

GCF(13305,13312) = 1
LCM(13305,13312) = ( 13305 × 13312) / 1
LCM(13305,13312) = 177116160 / 1
LCM(13305,13312) = 177116160

Least Common Multiple (LCM) of 13305 and 13312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13305 and 13312. First we will calculate the prime factors of 13305 and 13312.

Prime Factorization of 13305

Prime Factorization of 13312

Now multiplying the highest exponent prime factors to calculate the LCM of 13305 and 13312.

LCM(13305,13312) = 3¹ × 5¹ × 887¹ × 2¹⁰ × 13¹
LCM(13305,13312) = 177116160