Question

finn and gertrude made the same number of cupcakes for their valentines day party at school. finn made his cupcakes in batches of 10 and gertrude made her cupcakes in batches of 40. what is the smallest number of cupcakes that they each made? label optional

Explanation:

Step1: Identify the problem type

This is a problem of finding the least common multiple (LCM) of 10 and 40, as we need the smallest number that is a multiple of both 10 and 40 (since they made the same number of cupcakes).

Step2: Recall the formula for LCM of two numbers

If we have two numbers \(a\) and \(b\), and we know that \(b\) is a multiple of \(a\) (i.e., \(b = k\times a\) for some integer \(k\)), then the LCM of \(a\) and \(b\) is \(b\) itself.

Step3: Check the relationship between 10 and 40

We can see that \(40=4\times10\), which means 40 is a multiple of 10.

Step4: Determine the LCM

Since 40 is a multiple of 10, the least common multiple of 10 and 40 is 40.

Answer:

40