6 — Multiples and Common Multiples

Multiples and Common Multiples

Solution & Explanation · ID: 88B6347A

Question

A bakery makes cookies in batches of 8 and muffins in batches of 12. If they want to package equal numbers of cookies and muffins together, what is the smallest number of each they need to make?

Hint

Find the LCM of 8 and 12 to determine when they'll have equal amounts.

Concept

This is a real-world LCM problem. When we need equal quantities of items that come in different batch sizes, we find the LCM of the batch sizes to determine the smallest number of each item needed.

Show Answer

24 cookies and 24 muffins

Show Solution
1

Identify the batch sizes: cookies come in batches of 8, muffins come in batches of 12

2

To have equal numbers, we need to find the LCM of 8 and 12

3

List multiples of 8: 8, 16, 24, 32, 40...

4

List multiples of 12: 12, 24, 36, 48...

5

The LCM is 24, so they need 24 cookies (3 batches of 8) and 24 muffins (2 batches of 12)

Visual showing cookie batches and muffin batches. Left side shows 3 groups of 8 cookies each (8+8+8=24 cookies total). Right side shows 2 groups of 12 muffins each (12+12=24 muffins total). Both sides are connected with an equals sign showing '24 = 24' to demonstrate equal quantities.