What is the Least Common Multiple of 13740 and 13745?

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 13740 and 13745 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13740 and 13745, than apply into the LCM equation.

GCF(13740,13745) = 5
LCM(13740,13745) = ( 13740 × 13745) / 5
LCM(13740,13745) = 188856300 / 5
LCM(13740,13745) = 37771260

Least Common Multiple (LCM) of 13740 and 13745 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13740 and 13745. First we will calculate the prime factors of 13740 and 13745.

Prime Factorization of 13740

Prime Factorization of 13745

Now multiplying the highest exponent prime factors to calculate the LCM of 13740 and 13745.

LCM(13740,13745) = 2² × 3¹ × 5¹ × 229¹ × 2749¹
LCM(13740,13745) = 37771260