What is the Least Common Multiple of 13745 and 13750?

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 13745 and 13750 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13745 and 13750, than apply into the LCM equation.

GCF(13745,13750) = 5
LCM(13745,13750) = ( 13745 × 13750) / 5
LCM(13745,13750) = 188993750 / 5
LCM(13745,13750) = 37798750

Least Common Multiple (LCM) of 13745 and 13750 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13745 and 13750. First we will calculate the prime factors of 13745 and 13750.

Prime Factorization of 13745

Prime Factorization of 13750

Now multiplying the highest exponent prime factors to calculate the LCM of 13745 and 13750.

LCM(13745,13750) = 5⁴ × 2749¹ × 2¹ × 11¹
LCM(13745,13750) = 37798750