class six NCERT Maths question answer page number 68 w h a t have discussd
Answers
The last excesie 3.7 hole with answer and question thx
Step-by-step explanation:
Exercise 3.7 page no: 68
5. Determine the greatest 3-digit number exactly divisible by 8, 10 and 12.
Solutions:
LCM of 8, 10 and 12
NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 - 8
LCM = 2 × 2 × 2 × 3 × 5 = 120
Now we need to find the greatest 3-digit multiple of 120
We may find 120 × 8 = 960 and 120 × 9 = 1080
Hence, 960 is the greatest 3-digit number exactly divisible by 8, 10 and 12
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?
Solutions:
LCM of 48, 72, 108 = time period after which these lights change
NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 - 9
LCM = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432
Hence, lights will change together after every 432 seconds
Therefore the lights will change simultaneously at 7 minutes 12 seconds.
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.
Solutions:
HCF of 403, 434, 465 = Maximum capacity of tanker required
403 = 13 × 31
434 = 2 × 7 × 31
465 = 3 × 5 × 31
HCF = 31
Hence, a container of 31 litres can measure the diesel of the three containers exact number of times.
8. Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case.
Solutions:
LCM of 6, 15, 18
NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 - 10
LCM = 2 × 3 × 3 × 5 = 90
Required number = 90 + 5
= 95
Hence, 95 is the required number.
9. Find the smallest 4-digit number which is divisible by 18, 24 and 32.
Solutions:
LCM of 18, 24, 32
NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 - 11
LCM = 2 × 2 × 2 × 2 × 2 × 3 × 3 = 288
Here, we need to find the smallest 4-digit multiple of 288
We find 288 × 3 = 864 and 288 × 4 = 1152
Hence, 1152 is the smallest 4-digit number which is divisible by 18, 24 and 32
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?
Solutions:
(a) LCM of 9, 4
NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 - 12
LCM = 2 × 2 × 3 × 3 = 36
(b) LCM of 12, 5
NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 - 13
LCM = 2 × 2 × 3 × 5 = 60
(c) LCM of 6, 5
NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 - 14
LCM = 2 × 3 × 5 = 30
(d) LCM of 15, 4
NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 - 15
LCM = 2 × 2 × 3 × 5 = 60
Yes in each case the LCM of given numbers is the product of these numbers.
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?
Solutions:
(a) 5, 20
NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 - 16
LCM = 2 × 2 × 5 = 20
(b) 6, 18
NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 - 17
LCM = 2 × 3 × 3 = 18
(c) 12, 48
NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 - 18
LCM = 2 × 2 × 2 × 2 × 3 = 48
(d) 9, 45
NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 - 19
LCM = 3 × 3 × 5 = 45
∴ Hence, in each case the LCM of given numbers is the larger number. When a number is a factor of other number then their LCM will be the larger number.