EXERCISE 3.7
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.
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?
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
Determine the smallest 3-digit number which is exactly divisible by 6, 8 and 12.
Determine the greatest 3-digit number exactly divisible by 8, 10 and 12.
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?
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
Answers
Answer:
1. The weight of two bags are and .
The maximum weight will be the HCF of the given weights.
The factors of given weights are shown below.
The factors can be written as,
The HCF of the given numbers is .
Thus, the maximum value of weight that will measure the weight of the fertilizer exact number of times is .
2.The step measure of 1st boy is , the step measure of 2nd boy is and the step measures of 3rd boy is .
The minimum distance will be the LCM of the given step measures of the boys.
The LCM of the given numbers is shown below.
The factors can be written as,
Since, the LCM of the given numbers is .
Thus, each should cover the minimum distance of so that all can cover the distance in complete steps.
3.The length, breadth and height of a room are , and respectively.
Since, the longest tape will be the HCF of the given measurements.
The factors of numbers are,
Since, the common factors in the above numbers are , , so the HCF of the given numbers is .
Thus, the longest tape is
75
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cm
4.Since, the smallest three digit number that is exactly divisible by , , can be calculated by the LCM of , , .
The LCM of the given numbers is shown below.
Since, the LCM of the given numbers is .
The smallest three digit number can be written as,
Thus, the smallest three digit number that is exactly divisible by 6,8,12 is 120.
5.Since, the greatest three digit number that is exactly divisible by , , can be calculated by the LCM of the , , .
The LCM of the given numbers is shown below.
Since, the LCM of the given numbers is .
The greatest three digit multiple of is,
Thus, the greatest three digit number that is exactly divisible by ,8,10,12 is 920