What is the Least Common Multiple of 2240 and 2254?

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 2240 and 2254 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2240 and 2254, than apply into the LCM equation.

GCF(2240,2254) = 14
LCM(2240,2254) = ( 2240 × 2254) / 14
LCM(2240,2254) = 5048960 / 14
LCM(2240,2254) = 360640

Least Common Multiple (LCM) of 2240 and 2254 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2240 and 2254. First we will calculate the prime factors of 2240 and 2254.

Prime Factorization of 2240

Prime Factorization of 2254

Now multiplying the highest exponent prime factors to calculate the LCM of 2240 and 2254.

LCM(2240,2254) = 2⁶ × 5¹ × 7² × 23¹
LCM(2240,2254) = 360640