What is the least common multiple of 12, 7, 10 and 4?

To find the least common multiple (LCM) of 12, 7, 10, and 4, follow these steps:

1. First, find the prime factors of each number.

   • The prime factors of 12 are 2, 2, and 3.
   • The prime factors of 7 are 7.
   • The prime factors of 10 are 2 and 5.
   • The prime factors of 4 are 2 and 2.

2. Next, for each prime number, count the maximum number of times it appears in any of the factorizations.

   • The number 2 appears at most twice (in the factorization of 12 and 4).
   • The number 3 appears at most once (in the factorization of 12).
   • The number 5 appears at most once (in the factorization of 10).
   • The number 7 appears at most once (in the factorization of 7).

3. Multiply these counts by the corresponding prime numbers.

   • 2 * 2 = 4
   • 3 * 1 = 3
   • 5 * 1 = 5
   • 7 * 1 = 7

4. Finally, multiply these results together to get the LCM.

   • 4 * 3 * 5 * 7 = 420

So, the least common multiple of 12, 7, 10, and 4 is 420.