What is the Least Common Multiple of 40032 and 40040?

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 40032 and 40040 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40032 and 40040, than apply into the LCM equation.

GCF(40032,40040) = 8
LCM(40032,40040) = ( 40032 × 40040) / 8
LCM(40032,40040) = 1602881280 / 8
LCM(40032,40040) = 200360160

Least Common Multiple (LCM) of 40032 and 40040 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 40032 and 40040. First we will calculate the prime factors of 40032 and 40040.

Prime Factorization of 40032

Prime Factorization of 40040

Now multiplying the highest exponent prime factors to calculate the LCM of 40032 and 40040.

LCM(40032,40040) = 2⁵ × 3² × 139¹ × 5¹ × 7¹ × 11¹ × 13¹
LCM(40032,40040) = 200360160