can anyone please explain example 5 and 6? how do we know when to find LCM and when HCF?
The given examples explains the concept in a very simplified manner. Mention the specific step(s) in the solution which are not clear to you and get back to us. We will be happy to help you.
The HCF of two or more numbers is the largest common factor of the given numbers.
The LCM is the smallest number that is a common multiple of two or more numbers.
Let us take the example 5 of the study material:
Anurag takes 6 minutes to complete one round of jogging around the circular track of a park, while Twinkle takes 8 minutes to do the same. If both of them start jogging at the same time from the same point, then how much time will they take before they meet at the point from which they started?
Its solution can be given as,
Anurag and Twinkle take 6 minutes and 8 minutes respectively to complete one round of the circular track.
Anurag jogs around the circles after every 6 minutes i.e., he completes the one, two, three, four rounds around the park after 6 minutes, 12 minutes, 18 minutes, 24 minutes, 30 minutes respectively and so on.
Twinkle jogs around the circles after every 8 minutes i.e., she completes the one, two, three, four rounds around the park after 8 minutes, 16 minutes, 24 minutes, 32 minutes, 40 minutes respectively and so on.
You may observe that the smallest time after which they will meet at the starting point is 24 minutes. And you also know that 24 is the L.C.M. of 6 and 8.
Now, the thing is that without analysing what I have done above, how will you know that this question is based on L.C.M.?
It is quite simple. The time after which they meet must be greater than the time taken by them to complete one round. During that time, they have completed a number of rounds.
From this it is clear that the required time must be a common multiple of 6 minutes and 8 minutes. Since, you are required to find the least time, so, the required time must a least common multiple of 6 minutes and 8 minutes, I,e, L.C.M. of 6 minutes and 8 minutes.
In this way you have to analyse the situation given to you and figure out whether HCF or LCM needs to be taken to solve the given word problem.