What is the Least Common Multiple of 10032 and 10038?

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 10032 and 10038 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10032 and 10038, than apply into the LCM equation.

GCF(10032,10038) = 6
LCM(10032,10038) = ( 10032 × 10038) / 6
LCM(10032,10038) = 100701216 / 6
LCM(10032,10038) = 16783536

Least Common Multiple (LCM) of 10032 and 10038 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10032 and 10038. First we will calculate the prime factors of 10032 and 10038.

Prime Factorization of 10032

Prime Factorization of 10038

Now multiplying the highest exponent prime factors to calculate the LCM of 10032 and 10038.

LCM(10032,10038) = 2⁴ × 3¹ × 11¹ × 19¹ × 7¹ × 239¹
LCM(10032,10038) = 16783536