Page 65 - Start Up Mathematics_6

Example 41: Joseph, David and Tarun start walking from the same spot. Their steps measure
72 cm, 81 cm and 90 cm respectively. What is the minimum distance each should
cover so that all can cover the distance in complete steps?

Solution: Measure of their steps is 72 cm, 81 cm and 90 cm. Minimum distance each should
cover is obtained by finding the LCM of 72, 81 and 90. 2 72, 81, 90
Therefore, LCM = 2 × 3 × 3 × 4 × 9 × 5 = 3,240 3 36, 81, 45

Hence, the least distance that can be covered in 3 12, 27, 15
complete steps is 3,240 cm. 4, 9, 5

Example 42: Dolly purchases two bags of fertilizer weighing 75 kg and 105 kg. Find the maximum
value of weight which can measure the two bags exact number of times.
Solution: To find the maximum value of weight which

can measure bags of 75 kg and 105 kg exact Puzzle
number of times, we need to find the HCF of Determine the number of revolutions
75 and 105. gear 1 must make before the arrows
are lined up again.
All possible prime factors of 75 = 3 × 5 × 5
All possible prime factors of 105 = 3 × 5 × 7 Gear 1 Gear 2

The common factors of 75 and 105 are 3 and 5.
Therefore, HCF of 75 and 105 = 3 × 5 = 15. 24 teeth 28 teeth

Hence, the maximum value of weight required
to measure the bags is 15 kg.
Example 43: Determine the smallest 3-digit number which is exactly divisible by 6, 8 and 12.
(NCERT)

Solution: To get the desired number let’s first find the LCM of 6, 8 and 12.
The LCM of 6, 8 and 12 = 2 × 2 × 3 × 2 = 24 2 6, 8, 12

Now the multiples of 24 are 48, 72, 96, 120, 144, ..., etc. 2 3, 4, 6
Hence, the smallest 3-digit number which is exactly divisible by 3 3, 2, 3
6, 8 and 12 is 120. 1, 2, 1

Example 44: Determine the greatest 4-digit number which is exactly divisible by 8, 10 and 12.

Solution: To get the desired number let’s first find the LCM of 8, 10 and 12.
The LCM of 8, 10 and 12 = 2 × 2 × 2 × 5 × 3 = 120
2 8, 10, 12
Now, the multiples of 120 are 240, 360, 480, 600, ..., 9,840, 2 4, 5, 6
9,960, 10,080, ..., etc. 2, 5, 3
Hence, the greatest 4-digit number which is exactly divisible
by 8, 10 and 12 is 9,960.

Example 45: The traffic lights at three different road crossings change after every 48 seconds,
72 seconds and 108 seconds respectively. If they change simultaneously at 8 a.m.,
at what time will they change simultaneously again?

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