What is the Least Common Multiple of 13740 and 13749?

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 13749 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 13749, than apply into the LCM equation.

GCF(13740,13749) = 3
LCM(13740,13749) = ( 13740 × 13749) / 3
LCM(13740,13749) = 188911260 / 3
LCM(13740,13749) = 62970420

Least Common Multiple (LCM) of 13740 and 13749 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13740 and 13749. First we will calculate the prime factors of 13740 and 13749.

Prime Factorization of 13740

Prime Factorization of 13749

Now multiplying the highest exponent prime factors to calculate the LCM of 13740 and 13749.

LCM(13740,13749) = 2² × 3¹ × 5¹ × 229¹ × 4583¹
LCM(13740,13749) = 62970420