What is the Least Common Multiple of 13700 and 13705?

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 13700 and 13705 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13700 and 13705, than apply into the LCM equation.

GCF(13700,13705) = 5
LCM(13700,13705) = ( 13700 × 13705) / 5
LCM(13700,13705) = 187758500 / 5
LCM(13700,13705) = 37551700

Least Common Multiple (LCM) of 13700 and 13705 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13700 and 13705. First we will calculate the prime factors of 13700 and 13705.

Prime Factorization of 13700

Prime Factorization of 13705

Now multiplying the highest exponent prime factors to calculate the LCM of 13700 and 13705.

LCM(13700,13705) = 2² × 5² × 137¹ × 2741¹
LCM(13700,13705) = 37551700