Jaime's Stickers A Math Problem Solving Adventure

by Felix Dubois 50 views

Hey there, math enthusiasts! Today, we're diving into a fun little problem involving our friend Jaime and his awesome sticker collection. Jaime has a bunch of stickers, and he's been counting them in a rather peculiar way. He counts them in groups of 2, then in groups of 4, and finally in groups of 6. The cool thing is, no matter how he counts them, he never has any stickers left over. Our mission, should we choose to accept it, is to figure out exactly how many stickers Jaime has, given that he has between 30 and 40 stickers. Sounds like a fun challenge, right? Let's put on our thinking caps and get started!

Cracking the Code: Understanding the Problem

Okay, let's break down this sticker conundrum. The key piece of information here is that Jaime can count his stickers by 2s, 4s, and 6s without any leftovers. What does this tell us? Well, it means that the number of stickers he has must be divisible by 2, 4, and 6. In math lingo, we're looking for a number that is a multiple of 2, 4, and 6. Think of it like this: if you have a number of stickers that can be divided evenly into groups of 2, 4, and 6, you won't have any stragglers hanging around. This is our first clue, and it's a big one!

But that's not all we know. We also know that Jaime's sticker stash is somewhere between 30 and 40 stickers. This is our range, our boundaries, the walls of our sticker-solving playground. We can't just pick any multiple of 2, 4, and 6; it has to fall within this range. So, we're essentially looking for a number that fits two criteria: it's a multiple of 2, 4, and 6, and it's between 30 and 40. Now, how do we find such a magical number?

Finding the Least Common Multiple (LCM)

This is where the concept of the Least Common Multiple (LCM) comes into play. The LCM of a set of numbers is the smallest number that is a multiple of all the numbers in the set. In our case, we need to find the LCM of 2, 4, and 6. Why? Because the LCM will give us the smallest possible number of stickers that Jaime could have, which is divisible by 2, 4, and 6. From there, we can check if any multiples of the LCM fall within our 30-40 sticker range.

So, how do we find the LCM of 2, 4, and 6? There are a couple of ways to do this. One way is to list out the multiples of each number until we find a common one. Let's try that:

  • Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, ...
  • Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
  • Multiples of 6: 6, 12, 18, 24, 30, 36, 42, ...

Looking at these lists, we can see that the smallest number that appears in all three is 12. So, the LCM of 2, 4, and 6 is 12. This means that any number of stickers that is a multiple of 12 will be divisible by 2, 4, and 6.

Spotting the Solution: Multiples Within the Range

Now that we know the LCM is 12, we need to find multiples of 12 that fall between 30 and 40. Let's list out some multiples of 12:

  • 12 x 1 = 12
  • 12 x 2 = 24
  • 12 x 3 = 36
  • 12 x 4 = 48

Aha! We have a winner! The multiple 36 falls neatly within our 30-40 range. So, 36 is a number that is divisible by 2, 4, and 6, and it's within the number of stickers Jaime has.

The Grand Reveal: Jaime's Sticker Count

So, after all our mathematical sleuthing, we've cracked the code! Jaime has 36 stickers in his collection. How cool is that? We used the power of multiples, the LCM, and a little bit of logical deduction to solve this sticker mystery. Give yourselves a pat on the back, math detectives! You've earned it.

Why This Matters: The Power of Mathematical Thinking

Now, you might be thinking,