What is the Least Common Multiple of 27714 and 27728?

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 27714 and 27728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27714 and 27728, than apply into the LCM equation.

GCF(27714,27728) = 2
LCM(27714,27728) = ( 27714 × 27728) / 2
LCM(27714,27728) = 768453792 / 2
LCM(27714,27728) = 384226896

Least Common Multiple (LCM) of 27714 and 27728 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27714 and 27728. First we will calculate the prime factors of 27714 and 27728.

Prime Factorization of 27714

Prime Factorization of 27728

Now multiplying the highest exponent prime factors to calculate the LCM of 27714 and 27728.

LCM(27714,27728) = 2⁴ × 3¹ × 31¹ × 149¹ × 1733¹
LCM(27714,27728) = 384226896