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Let us understand this by considering the following situations:

Suppose a rabbit and a frog are jumping over the number line. The frog jumps 3 steps
each time, while the rabbit jumps 4 steps each time.

The frog jumps on the numbers 3, 6, 9, 12, ...

The rabbit jumps on the numbers 4, 8, 12, ...

Here, the frog and the rabbit both jump on point 12, so 12 is a common multiple of 3 and 4.

Now, consider another situation where a rat and a grasshopper are taking jumps of 3
and 6 units every time.

The rat jumps on 3, 6,9, 12, ...

The grasshopper jumps on 6, 12, ...

Common multiples are the points on the number line which both jump on. These are 6, 12, ...

Therefore, 6 and 12 are common multiples of 3 and 6.

example 1. Find the common multiples of 2 and 5.

Solution. Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...

Multiples of 5 = 5, 10, 15, 20, ...

Therefore, the common multiples of 2 and 5 are 10, 20, ...

Common Factors

Generally, 1 and the number itself are factors of any number. To find the remaining
factors, we need to rely on our number sense and multiplication tables.

Factors of 20 are the numbers by which 20 is divisible.

20 comes in the multiplication table of 2: 2 × 10 = 20, so 2 and 10 are its factors.

20 comes in the multiplication table of 4: 4 × 5 = 20, so 4 and 5 are its factors.

Hence, the factors of 20 are 1, 2, 4, 5, 10 and 20.

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