What is the Least Common Multiple of 13705 and 13724?

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 13724 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 13724, than apply into the LCM equation.

GCF(13705,13724) = 1
LCM(13705,13724) = ( 13705 × 13724) / 1
LCM(13705,13724) = 188087420 / 1
LCM(13705,13724) = 188087420

Least Common Multiple (LCM) of 13705 and 13724 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13705 and 13724. First we will calculate the prime factors of 13705 and 13724.

Prime Factorization of 13705

Prime Factorization of 13724

Now multiplying the highest exponent prime factors to calculate the LCM of 13705 and 13724.

LCM(13705,13724) = 5¹ × 2741¹ × 2² × 47¹ × 73¹
LCM(13705,13724) = 188087420