What is the Least Common Multiple of 13758 and 13770?

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 13758 and 13770 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13758 and 13770, than apply into the LCM equation.

GCF(13758,13770) = 6
LCM(13758,13770) = ( 13758 × 13770) / 6
LCM(13758,13770) = 189447660 / 6
LCM(13758,13770) = 31574610

Least Common Multiple (LCM) of 13758 and 13770 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13758 and 13770. First we will calculate the prime factors of 13758 and 13770.

Prime Factorization of 13758

Prime Factorization of 13770

Now multiplying the highest exponent prime factors to calculate the LCM of 13758 and 13770.

LCM(13758,13770) = 2¹ × 3⁴ × 2293¹ × 5¹ × 17¹
LCM(13758,13770) = 31574610