What is the Least Common Multiple of 13695 and 13700?

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 13695 and 13700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13695 and 13700, than apply into the LCM equation.

GCF(13695,13700) = 5
LCM(13695,13700) = ( 13695 × 13700) / 5
LCM(13695,13700) = 187621500 / 5
LCM(13695,13700) = 37524300

Least Common Multiple (LCM) of 13695 and 13700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13695 and 13700. First we will calculate the prime factors of 13695 and 13700.

Prime Factorization of 13695

Prime Factorization of 13700

Now multiplying the highest exponent prime factors to calculate the LCM of 13695 and 13700.

LCM(13695,13700) = 3¹ × 5² × 11¹ × 83¹ × 2² × 137¹
LCM(13695,13700) = 37524300