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Multiples of 22 are numbers like 22, 44, 66, 88, and so on. Multiples of 28 are numbers like 28, 56, 84, 112, etc. The smallest common multiple of both 22 and 28 is 308. So, common multiples include 308, 616, 924, and so forth.
Solution
Let’s break down the problem into parts:
1. Multiples of 22:
These are numbers you get by multiplying 22 by integers. For example:
22, 44, 66, 88, 110, 132, 154, 176, …
2. Multiples of 28:
Similarly, these come from multiplying 28 by integers. For example:
28, 56, 84, 112, 140, 168, 196, 224, …
3. Common Multiples of 22 and 28:
A common multiple is a number that is a multiple of both numbers. A handy way to find the common multiples is to use the Least Common Multiple (LCM).
Step A: Factorize each number.
22 = 2 × 11
28 = 2² × 7
Step B: The LCM is found by taking the highest powers of all prime factors present.
LCM = 2² × 7 × 11 = 4 × 77 = 308
So, the smallest (or least) common multiple of 22 and 28 is 308, and every common multiple will be a multiple of 308. In other words, a number is a multiple of both 22 and 28 if and only if it can be written as 308k, where k is an integer.
4. Examples of common multiples:
When k = 1, 308
When k = 2, 616
When k = 3, 924
… and so on.
To summarize:
• Multiples of 22 are: 22, 44, 66, 88, …
• Multiples of 28 are: 28, 56, 84, 112, …
• Common multiples of 22 and 28 are: 308, 616, 924, … (which are all multiples of 308)
This is how you find and describe the multiples of 22 and 28.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
Did you know that the least common multiple (LCM) of 22 and 28 is 308? This means that 308 is the smallest number that both 22 and 28 can divide evenly into. You can find multiples of both numbers by simply multiplying them by integers: for example, 22, 44, 66, 88, and so on for 22, while for 28, you could have 28, 56, 84, 112, and so forth. When working with multiples, a common mistake is forgetting to include zero. Remember, multiplying by zero gives you zero, which is a multiple of every number! And don't forget to use prime factorization as an alternative method for finding LCM. For 22, it's 2 and 11, and for 28, it’s 2, 2, and 7. Have fun playing with numbers!
