What is the Least Common Multiple of 27000 and 27014?

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 27000 and 27014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27000 and 27014, than apply into the LCM equation.

GCF(27000,27014) = 2
LCM(27000,27014) = ( 27000 × 27014) / 2
LCM(27000,27014) = 729378000 / 2
LCM(27000,27014) = 364689000

Least Common Multiple (LCM) of 27000 and 27014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27000 and 27014. First we will calculate the prime factors of 27000 and 27014.

Prime Factorization of 27000

Prime Factorization of 27014

Now multiplying the highest exponent prime factors to calculate the LCM of 27000 and 27014.

LCM(27000,27014) = 2³ × 3³ × 5³ × 13¹ × 1039¹
LCM(27000,27014) = 364689000