What is the Least Common Multiple of 13725 and 13740?

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 13725 and 13740 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13725 and 13740, than apply into the LCM equation.

GCF(13725,13740) = 15
LCM(13725,13740) = ( 13725 × 13740) / 15
LCM(13725,13740) = 188581500 / 15
LCM(13725,13740) = 12572100

Least Common Multiple (LCM) of 13725 and 13740 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13725 and 13740. First we will calculate the prime factors of 13725 and 13740.

Prime Factorization of 13725

Prime Factorization of 13740

Now multiplying the highest exponent prime factors to calculate the LCM of 13725 and 13740.

LCM(13725,13740) = 3² × 5² × 61¹ × 2² × 229¹
LCM(13725,13740) = 12572100