What is the Least Common Multiple of 13734 and 13752?

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 13734 and 13752 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13734 and 13752, than apply into the LCM equation.

GCF(13734,13752) = 18
LCM(13734,13752) = ( 13734 × 13752) / 18
LCM(13734,13752) = 188869968 / 18
LCM(13734,13752) = 10492776

Least Common Multiple (LCM) of 13734 and 13752 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13734 and 13752. First we will calculate the prime factors of 13734 and 13752.

Prime Factorization of 13734

Prime Factorization of 13752

Now multiplying the highest exponent prime factors to calculate the LCM of 13734 and 13752.

LCM(13734,13752) = 2³ × 3² × 7¹ × 109¹ × 191¹
LCM(13734,13752) = 10492776