Daniel is thinking of a number that is divisible by both 12 and 7. What is the smallest possible number that Daniel could be thinking of?

The smallest number that Daniel could be thinking of is the least common multiple (LCM) of 12 and 7.

Here are the steps to find the LCM:

1. Prime factorize the numbers:

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

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

   • The prime factor 2 occurs twice in 12 and not at all in 7, so write it down twice.
   • The prime factor 3 occurs once in 12 and not at all in 7, so write it down once.
   • The prime factor 7 occurs once in 7 and not at all in 12, so write it down once.

3. Multiply these prime factors together to get the LCM:

   • 2 * 2 * 3 * 7 = 84.

So, the smallest possible number that Daniel could be thinking of is 84.