Rob realizes that the number on the classroom door is divisible by 12, and his classmate points out that it is also divisible by 13. What is the smallest possible number that could be on the classroom door?
Question
Rob realizes that the number on the classroom door is divisible by 12, and his classmate points out that it is also divisible by 13. What is the smallest possible number that could be on the classroom door?
Solution
The smallest possible number on the classroom door would be the least common multiple (LCM) of 12 and 13.
Step 1: Identify the two numbers. In this case, the numbers are 12 and 13.
Step 2: Since 12 and 13 are both prime to each other (they have no common factors other than 1), the LCM of 12 and 13 is simply their product.
Step 3: Multiply 12 and 13 together.
12 * 13 = 156
So, the smallest possible number that could be on the classroom door is 156.
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