# Common Multiples

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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**5th Grade Math**

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