Question

Nina is printing orange and green forms. She notices that 12 orange forms fit on a page, and 3 green forms fit on a page. If Nina wants to print the exact same number of orange and green forms, what is the minimum number of each form that she could print?

Answer 1

To find the minimum number of orange and green forms that Nina could print such that the numbers are equal, we need to find the least common multiple (LCM) of the number of forms that fit on a page.

Nina can fit:
- 12 orange forms on a page
- 3 green forms on a page

We denote:
- \( O \) as the number of orange forms
- \( G \) as the number of green forms

We start with the equation relating the quantities of forms:
\[
O = 12k \quad \text{(for some integer } k\text{)}
\]
\[
G = 3m \quad \text{(for some integer } m\text{)}
\]

We want to find values of \( O \) and \( G \) such that \( O = G \). Thus:
\[
12k = 3m
\]

We can simplify this equation by dividing both sides by 3:
\[
4k = m
\]

This shows that \( m \) must be a multiple of 4 if \( k \) is an integer. For the smallest integers, let \( k = 1 \):
\[
m = 4 \times 1 = 4
\]

Now substituting back to find \( O \) and \( G \):
\[
O = 12k = 12 \times 1 = 12
\]
\[
G = 3m = 3 \times 4 = 12
\]

Thus, the minimum number of orange and green forms that Nina should print such that they are equal is:
\[
\boxed{12}
\]

To verify, both the orange and green forms total to 12, so indeed she can print them in equal quantities while respecting the capacity per page requirement.