What is the Least Common Multiple of 13705 and 13725?

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 13705 and 13725 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13705 and 13725, than apply into the LCM equation.

GCF(13705,13725) = 5
LCM(13705,13725) = ( 13705 × 13725) / 5
LCM(13705,13725) = 188101125 / 5
LCM(13705,13725) = 37620225

Least Common Multiple (LCM) of 13705 and 13725 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13705 and 13725. First we will calculate the prime factors of 13705 and 13725.

Prime Factorization of 13705

Prime Factorization of 13725

Now multiplying the highest exponent prime factors to calculate the LCM of 13705 and 13725.

LCM(13705,13725) = 5² × 2741¹ × 3² × 61¹
LCM(13705,13725) = 37620225