NCERT Solutions For Class 6 Maths Chapter 3

Playing With Numbers

NCERT Solutions For Class 6 Maths chapter 3 Exercise 3.7

Question 1

Renu purchases two bags of fertiliser of weights 75 kg and 69 kg. Find the maximum value of weight which can measure the weight of the fertiliser exact number of times.

Answer 1

Weight of two bags of fertiliser = 75 kg and 69 kg
For maximum weight
HCF of 75 and 69
Factor of 75 = 3 × 5 × 5
Factor of 69 = 3 × 23
HCF = 3
3 kg of weight can measure the weight of the fertiliser exact number of times.

Question2

Three boys step off together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm respectively. What is the minimum distance each should cover so that all can cover the distance in complete steps?

Answer 2

For minimum distance we need to find out LCM of 63cm,70cm and 77cm
First steps measure = 63 cm
Second steps measure = 70 cm
Third steps measure = 77 cm
LCM (70 , 77) = 2 × 3 × 3 × 5 × 7 × 11 = 6930
So, the minimum distance is 6930cm

Question 3

The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively. Find the longest tape which can measure the three dimensions of the room exactly.

Answer 3

Length of a room = 825 cm
Breadth of a room = 675 cm
Height of a room = 450 cm
Factor of 825 = 3 × 5 × 5 × 11
Factor of 675 = 3 × 3 × 3 × 5 × 5
Factor of 450 = 2 × 3 × 3 × 5 × 5
HCF = 3 × 5 × 5 = 75 cm
Hence longest tape is 75 cm.

Question 4

Determine the smallest 3-digit number which is exactly divisible by 6, 8 and 12.

Answer 4

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 - 7 LCM = 2 × 2 × 2 × 3 = 24
the smallest 3-digit 100
24 × 4 = 96 and 24 × 5 = 120
So, 120 is the smallest 3-digit number which is exactly divisible by 6, 8 and 12

Question 5

Determine the greatest 3-digit number exactly divisible by 8, 10 and 12.

Answer 5

LCM of 8, 10 and 12 LCM (8,10,12)= 2 × 2 × 2 × 3 × 5 = 120
the greatest 3-digit multiple of 999
999= 120 × 8 + 39
So the number is 999-39=960
So, 960 is the greatest 3-digit number divisible by 8, 10 and 12

Question 6

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds, respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?

Answer 6

LCM of 48, 72, 108
LCM(48,72,108) = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432
Here lights will change together after every 432 seconds
The lights will change at 7 minutes 12 seconds.

Question 7

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 exact number of times.

Answer 7

HCF of 403, 434, 465
Factor of 403 = 13 × 31
Factor of 434 = 2 × 7 × 31
Factor of 465 = 3 × 5 × 31
HCF = 31
Hence, a container of 31 litres are require to measure the quantity

Question 8

Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case.

Answer 8

LCM of 6, 15, 18
LCM(6,15,18) = 2 × 3 × 3 × 5 = 90
Required number = 90 + 5
So 95 is the required number.

Question 9

Find the smallest 4-digit number which is divisible by 18, 24 and 32.

Answer 9

LCM of 18, 24, 32
LCM(18, 24, 32) = 2 × 2 × 2 × 2 × 2 × 3 × 3 = 288
The smallest 4-digit number is 1000
On dividing 1000 by 288
1000=288 × 3+ 136
The require number is 1000 + (288 -136)= 1152

Question 10

Find the LCM of the following numbers: (a) 9 and 4 (b) 12 and 5 (c) 6 and 5 (d) 15 and 4
Observe a common property in the obtained LCMs. Is LCM the product of two numbers in each case?

Answer 10

(a) LCM of 9, 4
LCM(9,4) = 2 × 2 × 3 × 3 = 36
(b) LCM of 12, 5
LCM(12,5) = 2 × 2 × 3 × 5 = 60
(c) LCM of 6, 5
LCM (6,5)= 2 × 3 × 5 = 30
(d) LCM of 15, 4
LCM(15,4) = 2 × 2 × 3 × 5 = 60
Yes in each case the LCM of given numbers is the product of these numbers.

Question 11

Find the LCM of the following numbers in which one number is the factor of the other. (a) 5, 20 (b) 6, 18 (c) 12, 48 (d) 9, 45
What do you observe in the results obtained?

Answer 11

(a) 5, 20
LCM(5,20) = 2 × 2 × 5 = 20
(b) 6, 18
LCM(6,18) = 2 × 3 × 3 = 18
(c) 12, 48
LCM(12,48) = 2 × 2 × 2 × 2 × 3 = 48
(d) 9, 45
LCM(9,45) = 3 × 3 × 5 = 45
When a number is a factor of other number, then their LCM will be the larger number.