This topic would deal with common multiples. If some of the multiples of two or more number are same then those same multiples are termed as common multiples.
Here are few examples illustrating common multiples:
1. List the two common multiples of 5 and 6
Solution:
The multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60 …
The multiples of 6 are: 6, 12, 18, 24, 30, 42, 48, 54, 60, 66, 72, 78…
Hence, the common multiples of 5 and 6 are 30 and 60
So, we can see that both 30 and 60 is divisible by 5 and 6
2. Find the ten common multiples of 2 and 4
Solution:
The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 …
The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44 …
Hence, the ten common multiples of 2 and 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, and 40
So, we can see all ten common multiples are divisible by 2 and 4
3. Find the three common multiples of 6 and 8
Solution:
The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78 …
The multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88…
Hence, the three common multiples of 6 and 8 are 24, 48, and 72
So, we can see that all 24, 48, and 72 is divisible by 6 and 8
4. List the five common multiples of 5 and 10
Solution:
The multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60 …
The multiples of 10 are: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 …
Hence, the five common multiples of 5 and 10 are 10, 20, 30, 40, and 50
So, we can see all 10, 20, 30, 40, and 50 is divisible by 5 and 10
5. Find the five common multiples of 2, 4 and 6
Solution:
The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48 …
The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56 …
The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78 …
Hence, the five common multiples of 2, 4 and 6 are 6, 12, 24, 36, and 48
So, we can see all 6, 12, 24, 36, and 48 is divisible by 5 and 10
6. Find the first three common multiples of 14 and 16
Solution:
The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144…..
The multiples of 16 are: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192….
Hence the first three common multiples of 12 and 16 are: 48, 96, 144
So, we can see that all 48, 96, and 144 is divisible by 12 and 16
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