Playing with Numbers

Exercise 3.7

1). Find the HCF of the following numbers:

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

2). 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?

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

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

5). Determine 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 am at what time will they change simultaneously again?

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.

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

9). Find 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?

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?