What is the least common multiple of 40 and 27?

To find the least common multiple (LCM) of 40 and 27, follow these steps:

1. Prime factorize the two numbers.

   • The prime factors of 40 are 2, 2, 2, and 5.
   • The prime factors of 27 are 3, 3, and 3.

2. Write down each factor the greatest number of times it occurs in either factorization.

   • The factor 2 occurs three times in the factorization of 40 and zero times in the factorization of 27. So, write down 2 three times.
   • The factor 3 occurs zero times in the factorization of 40 and three times in the factorization of 27. So, write down 3 three times.
   • The factor 5 occurs once in the factorization of 40 and zero times in the factorization of 27. So, write down 5 once.

3. Multiply all the factors together to get the LCM.

   • 2 * 2 * 2 * 3 * 3 * 3 * 5 = 1080

So, the least common multiple of 40 and 27 is 1080.