What is the Least Common Multiple of 8 and 240?

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 8 and 240 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8 and 240, than apply into the LCM equation.

GCF(8,240) = 8
LCM(8,240) = ( 8 × 240) / 8
LCM(8,240) = 1920 / 8
LCM(8,240) = 240

Least Common Multiple (LCM) of 8 and 240 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8 and 240. First we will calculate the prime factors of 8 and 240.

Prime Factorization of 8

Prime Factorization of 240

Now multiplying the highest exponent prime factors to calculate the LCM of 8 and 240.

LCM(8,240) = 2⁴ × 3¹ × 5¹
LCM(8,240) = 240