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3. Find the HCF using the prime factorisation method Verify your answer using the
common division method.

(a) 15, 24 (b) 18, 90 (c) 32, 40 (d) 42, 56
(e) 15, 95 (f) 72, 80 (g) 12, 24, 48 (h) 22, 33, 66

(i) 24, 36, 56 (j) 22, 66, 99 (k) 25, 40, 65 (l) 48, 72, 96

4. Find the HCF using the long division method.

(a) 21, 63 (b) 35, 49 (c) 92, 132 (d) 36, 54, 72

(e) 132, 140, 250 (f) 165, 285, 205 (g) 164, 180, 112 (h) 285, 350, 1875

5. A fruit-seller has 1320 apples and 1480 mangoes. He wants to put them in baskets.
What is the greatest number of baskets required, if each basket has the same number
of apples and mangoes?

6. Find the largest possible length of a stick which can be used to measure 448 cm,
560 cm and 920 cm exactly.
7. A drum contained 220 litres of oil and another drum contained 336 litres of oil. What
capacity should the container be to take out the maximum amount of oil from both
the drums at the same time?

LOWEST COMMON MULTIPLE (LCM)

Let us take any two numbers, say 4 and 6 and list multiples of 4 and 6.

Multiples of 4 are 4, 8, 12 , 16, 20, 24 , ...
Multiples of 6 are 6, 12 , 18, 24 , ...

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

Common multiples of 4 and 6 are 12, 24, ...
Remember
The lowest common multiple (LCM) of 4 and 6 is 12. When a number is a multiple
of two or more numbers,
Thus, the smallest number which is a multiple of two or more then it is called a common
given numbers is called the least common multiple (LCM). multiple of those numbers.

Methods of Finding LCM

We can find the LCM by using any of the three methods:

(i) Common multiples method (ii) Prime factorisation method

(iii) Division method

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