Question

The scenario in a word problem states that an office supply store sells pens in packages of 12 and pencils in packages of 20. Which of the following questions about the scenario involves finding a common multiple of 12 and 20?

A. "How many pencils are in a package?"
B. "What is the total number of items in a package of pens and a package of pencils?"
C. "If I buy 24 pens, how many pencils do I need to buy to have an equal number of each?"
D. "What is the least number of pens and pencils I need to buy to have an equal number of each?"

Answer 1

The question from the scenario that requires finding a common multiple of 12 and 20 is related to purchasing an equal amount of pens and pencils, involving the least common multiple (LCM).

Step-by-step explanation:

Finding a common multiple of two numbers is a mathematical problem typically solved in arithmetic and number theory. When considering the scenario provided, where an office supply store sells pens in packages of 12 and pencils in packages of 20, the question that involves finding a common multiple of 12 and 20 is: "What is the least number of pens and pencils I need to buy to have an equal number of each?" The logic behind this relates to the concept of the least common multiple (LCM), which is the smallest positive integer that is a multiple of both 12 and 20.

To solve this practical problem, one would calculate the LCM of 12 and 20 to determine the smallest number of each item that can be purchased so that the total count of pens and pencils is the same. This common multiple tells us how many total items (packages or units) need to be bought to ensure an equal amount of both pens and pencils.