What is the Least Common Multiple of 13505 and 13514?

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 13505 and 13514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13505 and 13514, than apply into the LCM equation.

GCF(13505,13514) = 1
LCM(13505,13514) = ( 13505 × 13514) / 1
LCM(13505,13514) = 182506570 / 1
LCM(13505,13514) = 182506570

Least Common Multiple (LCM) of 13505 and 13514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13505 and 13514. First we will calculate the prime factors of 13505 and 13514.

Prime Factorization of 13505

Prime Factorization of 13514

Now multiplying the highest exponent prime factors to calculate the LCM of 13505 and 13514.

LCM(13505,13514) = 5¹ × 37¹ × 73¹ × 2¹ × 29¹ × 233¹
LCM(13505,13514) = 182506570