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4. Find the HCF using the long division method.
a. 24, 30 b. 32, 80 c. 60, 90 d. 30, 34

e. 49, 56 f. 24, 78 g. 14, 28, 70 h. 36, 54, 72
i. 15, 60, 106 j. 28, 70, 84 k. 64, 80, 112 l. 36, 72, 108

loWeST CoMMoN MulTiPle (lCM)

When a number is a multiple of two or more numbers, it is called their common
multiple. The smallest number among the common multiples is called the Lowest
Common Multiple (LCM).

Consider any two numbers, say 4 and 6. Let us list multiples of 4 and 6.
Look at the given number line. It shows some multiples of 4 and 6.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Multiples of 4 are 4, 8, 12, 16, 20, 24, ...

Multiples of 6 are 6, 12, 18, 24, ...
Common multiples of 4 and 6 are 12, 24, ...

The lowest common multiple or LCM of 4 and 6 is 12.
Methods to Find the lCM

There are different methods to find LCM. Here, we will study the listing multiples method.
listing Multiples Method

Write the multiples of the given numbers. Find their common multiples and choose
the smallest one.

example 1. Find the LCM of 15 and 20 using the listing multiples method.
Solution.

Step 1. Write some multiples of the first number, that is 15.

Multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, ...
Step 2. Write some multiples of the second number, that is 20.

Multiples of 20 are 20, 40, 60, 80, 100, 120, ...

Step 3. List the common multiples of both the numbers.
Common multiples of 15 and 20 are 60, 120, ...

Step 4. The smallest common multiple is the required LCM.
Thus, the least/lowest common multiple (LCM) of 15 and 20 is 60.

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Multiples and Factors