# Class 5 Mathematics | Chapter 6 Solutions | Be My Multiple; I Will Be Your Factor

The chapter 6 of class 5 NCERT mathematics is about factors and multiples. Here we have got practice problems and exercises to help students learn this chapter more easily.

More practice problems for this chapter can be found here and here.

## CLASS 5 CHAPTER 6 | Be My Multiple, I’ll be Your Factor

Fill in the blanks.

1. …………….is a factor of all numbers.

2. Highest factor of 12 is ……………..

3. The LCM of 2 and 6 is ………….

4. ………….. is the HCF of 3 and 9

5. The smallest factor of 6 is ……………………

6. The smallest common multiple of 12 and 15 is…………….

7. The highest common factor of 3 and 4 is…………….

8. The smallest multiple of 4 is……………

9. The biggest factor of a number is ………………

10. The exact divisor of a number is it’s…………..

1. One

2. Twelve

3. Six

4. Three

5. One

6. Sixty

7. One

8. Four

9. Same number

10. Factor

1. Find the common multiples of;

a. 3 and 4
b. 6 and 8
c. 7 and 9

Solution:

a. Multiples of 3 are 3,6,9,12,15,18,21,24,27,30,33,36……………..

Multiples of 4 are 4,8,12,16,20,24,28,32,36,40……………………
Common multiples are 12, 24, 36…………

b. Multiples of 6 are 6,12,18,24,30,36,42,48,54,60……………………..

Multiples of 8 are 8,16,24,32,40,48,56, 64, 72, 80……………………
Common multiples are 24, 48……….

c. Multiples of 7 are 7,14,21,28,35,42,49,56,63,70…………….

Multiples of 9 are 9,18,27,36,45,54,63,72,81,90…………….
Common multiples are 63………

2. Find the LCM of 3 and 5

Solution:

Multiples of 3 are 3,6,9,12,15,18,21,24,27,30…………..
Multiples of 5 are 5,10,15,20,25,30,35,40,45,50…………….

Common multiples are 15, 30………..

Least Common Multiple LCM = 15

3. Find the LCM of 10 and 20

Multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90,100………………….
Multiples of 20 are 20, 40, 60, 80,100,120,140……………

Common multiples are 20, 40, 60, 80, 100…………..

LCM = 20

4. Find the common factors of the numbers

a. 18 and 21
b. 12 and 15
c. 24 and 36

Solution:

a. Factors of 18 are 1, 18, 2, 9, 3, and 6

Factors of 21 are 1, 21, 3, and 7
Common factors are 1, 3

b. Factors of 12 are1, 12, 2,6,3,4

Factors of 15 are 1, 15, 3, and 5
Common factors are 1, 3

c. Factors of 24 are 1,24,2,12,3,8,4,6

Factors of 36 are 1, 36,2,18,3,12,4,9,6
Common factors are 1, 2,3,4,6

5. Find the HCF of 42 and 48

Solution:

Factors 42 are 1, 42, 2, 21, 6, 7
Factors of 48 are 1,48,2,24,3,16,4,12,6,8

Common factors are 1, 2, 6

Highest Common Factor HCF = 6

6. A path is tiled in 3 rows; the first row is done with 2 feet tiles, the second row with 3 feet tiles and the third one with 4 feet tiles. If none of these tiles are cut, what is the shortest length of the path?

Solution:

Shortest length of the path means LCM of these 3 numbers

Length of tile in the first row = 2, 4, 6, 8, 10, 12…………..
Length of tile in the second row = 3, 6, 9, 12, 15, 18, 21, 24, 27………………..
Length of tile in the third row = 4, 8, 12, 16, 20, 24, 28………………..

Shortest length of the path = LCM of 2, 3 and 4 = 12

7. The school math club meets every fifth day and English club meets every sixth day. They meet together on August 1.Find the day they meet together next?

Solution:

Days on which math club meets = 1, 6, 11, 16,21,26,31
Days on which English club meets = 1,7,13,19,25,31

The day they meet together next is on August 31.

8. There is a garden in Anu’s house. In the middle of the garden there is a path. They decided to tile the path using tiles of length 2 feet, 3 feet and 5 feet. The mason tiled the first row with 2 feet tiles, the second row with 3 feet tiles and the third row with 5 feet tiles. The mason has not cut any of the tiles. Then what is the shortest length of the path?

Solution:

Shortest length of the path = LCM of these numbers

Multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30…………….
Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30………………..
Multiples of 5 are 5, 10, 15, 20, 25, 30…………

The smallest common multiple is 30.

Hence the answer is 30 feet.

9. Manoj has made a new house. He wants to lay tiles on the floor. The size of the room is 9 feet x 12 feet. In the market, there are three kinds of square tiles: 1 foot x 1 foot, 2 feet x 2 feet and 3 feet x 3 feet. Which size of tile should he buy for his room, so that he can lay it without cutting?

Solution:

1 and 3 are factors of both 9 and 12.
2 is not a factor of 9 which is the width of the room.

Hence Manoj can buy tiles of 1 foot x 1 foot or 3 feet x 3 feet.

10. Rani , Geetha and Naseema live near each other. The distance from their houses to the road is 90 feet. They decided to tile the path to the road. They all bought tiles of different designs and length.Rani bought the shortest tile,Geetha bought the middle sized one and Naseema bought the longest one. If they could tile the path without cutting any of the tiles, what is the size of the tiles each has bought? Suggest 3 different solutions. Explain how you get this answer.

Solution:

The possible factors of 90 are

1, 90
2, 45
3, 30
5, 18
6, 15
9, 10

Hence the possible tiles can be as follows

1×1, 2×2, 3×3, 5×5, 6×6 etc.