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Step 4: In case of more than two numbers, first, find the HCF of any two given numbers and
then take the third number as dividend and the HCF obtained earlier as divisor. Repeat the
same process as did earlier till the remainder is zero.

Hence, the last divisor is the required HCF of more than two numbers.

Example 23: Find the HCF of 91 and 112.
Solution: By long division method,

9 112 1
– 91 Quick Check
Last divisor 21 91 4
– 84 1. Find the HCF of (a) 16, 64 and 88 (b) 120 and 168
7 21 3 2. What is the HCF of two consecutive (a) numbers?
– 21 (b) even numbers? (c) odd numbers?
0

Thus, the HCF of 91 and 112 is 7.
Example 24: Three tankers contain 403 litres, 434 litres and 465 litres of diesel respectively. Find
the maximum capacity of a container that can measure the diesel of the three containers an exact
number of times.

Solution: The capacity of the required container would be the HCF of 403 litres, 434 litres and 465
litres.

By using the long division method, first find the HCF of 403 and 434.

403 434 1 Now, find the HCF of 31 and 465.
– 403
31 403 13 31 465 15
– 31 – 31
Last divisor 93 155
– 93 – 155
0 0

So, 31 is the HCF of 403 and 434. Thus, 31 is the HCF of 403, 434 and 465.

Hence, the maximum capacity of the required container that can measure the diesel of the three
containers an exact number of times is 31 litres.

Lowest Common Multiple

Multiples of 10 Multiples of 15
We are familiar with the common multiples of two or more numbers.
Let us now try to find the lowest of these common multiples. 10 20 15

Consider the common multiples of 10 and 15. 30
50 60 45
They are 30, 60, 90,… 40
75
The lowest of these common multiples is 30. 70

So, 30 is called the lowest common multiple (LCM) of 10 and 15. Common multiples of 10 and 15

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