What is the Least Common Multiple of 17880 and 17888?

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 17880 and 17888 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17880 and 17888, than apply into the LCM equation.

GCF(17880,17888) = 8
LCM(17880,17888) = ( 17880 × 17888) / 8
LCM(17880,17888) = 319837440 / 8
LCM(17880,17888) = 39979680

Least Common Multiple (LCM) of 17880 and 17888 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17880 and 17888. First we will calculate the prime factors of 17880 and 17888.

Prime Factorization of 17880

Prime Factorization of 17888

Now multiplying the highest exponent prime factors to calculate the LCM of 17880 and 17888.

LCM(17880,17888) = 2⁵ × 3¹ × 5¹ × 149¹ × 13¹ × 43¹
LCM(17880,17888) = 39979680