Page 59 - ICSE Math 6

(b) Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, ...
Multiples of 18 are 18, 36, 54, 72, 90, 108, ...

First three common multiples of 12 and 18 are 36, 72 and 108.

Example 14: Write all the numbers less than 100, which are the common multiples of 3, 4 and 6.
Solution: Multiples of 3, 4 and 6 which are less than 100 are given below.
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60,
63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96 and 99.

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76,
80, 84, 88, 92 and 96.

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90 and 96.
Therefore, the common multiples of 3, 4 and 6 (less than 100) are 12, 24, 36, 48, 60,
72, 84 and 96.

Example 15: Which of the following pairs of numbers are co-prime?
(a) 9 and 16 (b) 25 and 420

Solution: (a) All possible factors of 9 are 1, 3 and 9.
All possible factors of 16 are 1, 2, 4, 8 and 16.
Clearly, 1 is the only common factor of 9 and 16. Therefore, 9 and 16 are co-prime.

(b) All possible factors of 25 are 1, 5 and 25.
All possible factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35,
42, 60, 70, 84, 105, 140, 210 and 420.
Clearly, 25 and 420 have common factors other than 1. Therefore, 25 and 420 are
not co-prime.

Points to remember

• If a number divides a given number then all of its factors will also divide the given number.
• If two co-prime numbers divide a given number then the product of co-prime numbers will also
divide the given number.
• If a number divides two given numbers then it will also divide their sum and difference.

EXERCISE 4.3

1. Find the common factors of:

(a) 10 and 15 (b) 16 and 20 (c) 21 and 35 (d) 3, 6 and 9
(e) 8, 12 and 20 (f) 45, 60 and 105
2. Find the first three common multiples of:

(a) 8 and 12 (b) 6 and 9 (c) 10 and 25
3. Write all the numbers less than 90, which are the common multiples of 5 and 6.
4. Which of the following pairs of numbers are co-prime?

(a) 13 and 16 (b) 16 and 21 (c) 25 and 105

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