Question

In separate rows in your garden, you plant onions 4 inches apart, peas 12 inches apart, and peppers 20 inches apart. The plants all line up at the beginning f the rows. How many inches will it be before all three vegetable line up again?

Answer 1

The question asks for the common multiple in inches where onions, peas, and peppers planted at different spacings will line up again. By listing the multiples of each spacing (4, 12, and 20), we find that the Least Common Multiple (LCM) is 60 inches, where all three types of plants will align once more.

Step-by-step explanation:

The student is asking about the common multiple, in inches, where onions, peas, and peppers planted in separate rows will line up again given that they are planted 4 inches, 12 inches, and 20 inches apart, respectively. To find the distance where all three vegetables will line up again, we need to calculate the Least Common Multiple (LCM) of their spacing.

• Onions are planted 4 inches apart.
• Peas are planted 12 inches apart.
• Peppers are planted 20 inches apart.

First, list the multiples of each spacing:

• Onion multiples: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
• Pea multiples: 12, 24, 36, 48, 60, ...
• Pepper multiples: 20, 40, 60, 80, ...

The LCM of 4, 12, and 20 is the smallest multiple they all share, which is 60.

Therefore, the plants will line up again after 60 inches, which is the LCM of their planting distances.