How will we know that when to take hcf or lcm in word problems of real numbers Class 10
Answers
There is no trick that can be applied to real numbers word problems. but...
The biggest mistake people do is to relate words present in the question with the abbreviation HCF and LCM.
Knowing this fact is tough to digest and only makes things harder... try practicing all the different types of tricky word problems to understand the relation.
Though, there are a few things you can look for in a question to make things easier:
- Look for terms like equally, exactly, etc
- From your understanding of the question, try judging whether the answer is greater or lesser than the given data... i.e
HCF - Highest Common Factor
LCM - Lowest Common Multiple
Now,
[a factor is a number that divides another number equally],
[a multiple a product of two numbers (one being certain and one variable)]
-> this means that a multiple is greater than a factor. (in comparison only)
This is tricky because the full form of HCF includes highest and LCM includes lowest but, a multiple is greater than a factor.
Conclusion:
1. HCF - despite having the term "highest", it only means the maximum limit of a possible factor within the given data's range.
In short, highest limit of a small number.
2. LCM - despite having the term "lowest", it only means the minimum limit of a possible multiple within the given data's range.
In short, lowest limit of a larger number.
3. From 1. and 2. we can say that HCF < LCM. (remember, this is only in the case of comparison of both the terms)
With this information and the requirement of the question we can guess whether the answer is supposed to be smaller or greater.
eg: We have three traffic signals at different road crossings that change simultaneously at a certain time. All the three signals have different times of changing: 4 minutes, 12 minutes and 16 minutes respectively. After how much time will they change simultaneously again?
= by this question we can understand that the 1st traffic light goes off after every 4 minutes, 2nd traffic light goes off after every 12 minutes and the 3rd traffic light goes off after every 16 minutes.
Now, if a traffic lights time intervals is lesser than the other (let's take 4 minutes), it would be obvious that a traffic light with a time interval of anything greater (12 minutes or 16 minutes > 4 minutes) than the initial chosen data (4 minutes) won't be able to obtain a time interval of 4 minutes (a technical issue is exceptional and not included), it's physically not possible.
This observations says that the next time they'll light up simultaneously would be greater that the given values. Therefore, we take the lcm of 4, 12 and 16.
LCM (4, 12, 16) = [HCF * remaining numbers] = 4 * 2 * 2 * 3 = 48
4 = 2 * 2 * 1
12 = 2 * 2 * 3 * 1
16 = 2 * 2 * 2 * 2 * 1
Therefore, the three traffic lights will change simultaneously again after 48 minutes.
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I tried my best to explain it, I apologize if the presentation is confusing. I hope you understand, if you have any troubles regarding this response feel free to inquire and question.
p.s I made the question (cause I forgot the real question but still tried to relate it) so I apologize in advance for any error.