Adam drew two same size rectangles and divided them into equal parts. He shaded 1/3 of one rectangle and 1/4 of other rectangle. What is the least number of parts into which both rectangles could be divided?

To find the answer to this problem, we need to figure out what number can be divided by 3 and 4 at the same time?

In math, that number is called a common multiple; there are more than one common multiple for 3 and 4, but we need to find the smallest ("What is the least number of parts...")

The smallest common multiple for 3 and 4 is 12.

So, the least number of parts in which both rectangles could be divided is 12

Other numbers that could be divided by 3 and 4 at the same time are 24, 48 etc, but the smallest is 12.

But could it be divided by 12?

12 Oh, rectangles, always trying to one-up each other with the number of parts. Well, don't worry, I've got just the joke for this occasion!

Why did the rectangle go on a diet?
Because it wanted to have fewer partitions!

Now, back to your question. To find the least number of parts into which both rectangles could be divided, we need to find the least common multiple (LCM) of the denominators 3 and 4. In this case, the LCM is 12.

So, the rectangles could be divided into 12 equal parts each.

To find the least number of parts into which both rectangles can be divided, we need to find the least common multiple (LCM) of the denominators of the shaded parts, which are 3 and 4.

To find the LCM of 3 and 4, we can list out the multiples of both numbers and find their common multiple:

Multiples of 3: 3, 6, 9, 12, 15, 18, ...

Multiples of 4: 4, 8, 12, 16, 20, 24, ...

From this list, we can see that the common multiple of 3 and 4 is 12. Therefore, the least number of parts into which both rectangles can be divided is 12.

This means that each rectangle needs to be divided into 12 equal parts, and then we can shade 1/3 of one rectangle (which would be 4 parts) and 1/4 of the other rectangle (which would be 3 parts).

So, the answer is that the least number of parts into which both rectangles could be divided is 12.