Question

List all the common multiples of 7 and 14 that are less than 60 .

Short answer

14, 28, 42, 56

Step-by-step solution

Identify Multiples of 7

List the multiples of 7 that are less than 60: 7, 14, 21, 28, 35, 42, 49, 56

Identify Multiples of 14

List the multiples of 14 that are less than 60: 14, 28, 42, 56

Find Common Multiples

Compare the lists from Step 1 and Step 2 to identify the common multiples: Common multiples are 14, 28, 42, 56.

Key concepts

multiples of 7

Multiples of 7 are found by multiplying 7 by different whole numbers. For example, multiplying 7 by 1 gives us 7, multiplying 7 by 2 gives us 14, and so on. This series continues, giving a list of multiples: 7, 14, 21, and so forth.
It's useful to recognize these patterns when working through problems. By listing out the multiples of 7 up to a maximum number (like 60), you can see that they appear at regular intervals: 7, 14, 21, 28, 35, 42, 49, 56.

• 7 is 7x1
• 14 is 7x2
• 21 is 7x3
• 28 is 7x4
• 35 is 7x5
• 42 is 7x6
• 49 is 7x7
• 56 is 7x8

Knowing these multiples can simplify many problems, including finding common multiples with other numbers.

multiples of 14

Multiples of 14 are numbers that you get by multiplying 14 by whole numbers. If you multiply 14 by 1, you get 14. If you multiply 14 by 2, you get 28, and so on. This pattern of multiplication gives us a neat list: 14, 28, 42, and 56.
Again, these multiples show up at consistent intervals when we list them:

• 14 is 14x1
• 28 is 14x2
• 42 is 14x3
• 56 is 14x4

By practicing finding multiples of 14, you become quicker at recognizing them and can more easily solve related math exercises. It's crucial in some exercises to list these multiples to help find commonalities with the multiples of other numbers.

comparing multiples

Comparing multiples means finding numbers that appear in the list of multiples of two or more different numbers. For example, to find common multiples of 7 and 14, first, list the multiples of each number:

• Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56
• Multiples of 14: 14, 28, 42, 56

Next, look for numbers that show up in both lists. These are the common multiples. In this case, the common multiples are 14, 28, 42, and 56.
This is a useful skill to have because it helps you see the relationships between different numbers and their multiples. Knowing how to compare multiples can also help with various math problems, including those involving least common multiples (LCM) and greatest common divisors (GCD). It's all about finding patterns and understanding how numbers relate to each other.