What is the Least Common Multiple of 90 and 270?

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 90 and 270 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90 and 270, than apply into the LCM equation.

GCF(90,270) = 90
LCM(90,270) = ( 90 × 270) / 90
LCM(90,270) = 24300 / 90
LCM(90,270) = 270

Least Common Multiple (LCM) of 90 and 270 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90 and 270. First we will calculate the prime factors of 90 and 270.

Prime Factorization of 90

Prime Factorization of 270

Now multiplying the highest exponent prime factors to calculate the LCM of 90 and 270.

LCM(90,270) = 2¹ × 3³ × 5¹
LCM(90,270) = 270