What is the Least Common Multiple of 270 and 278?

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 270 and 278 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 270 and 278, than apply into the LCM equation.

GCF(270,278) = 2
LCM(270,278) = ( 270 × 278) / 2
LCM(270,278) = 75060 / 2
LCM(270,278) = 37530

Least Common Multiple (LCM) of 270 and 278 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 270 and 278. First we will calculate the prime factors of 270 and 278.

Prime Factorization of 270

Prime Factorization of 278

Now multiplying the highest exponent prime factors to calculate the LCM of 270 and 278.

LCM(270,278) = 2¹ × 3³ × 5¹ × 139¹
LCM(270,278) = 37530