What is the Least Common Multiple of 17946 and 17952?

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 17946 and 17952 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17946 and 17952, than apply into the LCM equation.

GCF(17946,17952) = 6
LCM(17946,17952) = ( 17946 × 17952) / 6
LCM(17946,17952) = 322166592 / 6
LCM(17946,17952) = 53694432

Least Common Multiple (LCM) of 17946 and 17952 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17946 and 17952. First we will calculate the prime factors of 17946 and 17952.

Prime Factorization of 17946

Prime Factorization of 17952

Now multiplying the highest exponent prime factors to calculate the LCM of 17946 and 17952.

LCM(17946,17952) = 2⁵ × 3² × 997¹ × 11¹ × 17¹
LCM(17946,17952) = 53694432