What is the Least Common Multiple of 30240 and 30248?

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 30240 and 30248 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30240 and 30248, than apply into the LCM equation.

GCF(30240,30248) = 8
LCM(30240,30248) = ( 30240 × 30248) / 8
LCM(30240,30248) = 914699520 / 8
LCM(30240,30248) = 114337440

Least Common Multiple (LCM) of 30240 and 30248 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30240 and 30248. First we will calculate the prime factors of 30240 and 30248.

Prime Factorization of 30240

Prime Factorization of 30248

Now multiplying the highest exponent prime factors to calculate the LCM of 30240 and 30248.

LCM(30240,30248) = 2⁵ × 3³ × 5¹ × 7¹ × 19¹ × 199¹
LCM(30240,30248) = 114337440