# HOW TO SOLVE HCF AND LCM WORD PROBLEMS

## About the topic "How to solve hcf and lcm word problems"

"How to solve hcf and lcm word problems ?" is a big question having had by the people who get prepared for competitive exams and study quantitative aptitude. For some students, solving word problems on hcf and lcm is never being easy and always it is a challenging one.

## How to solve hcf and lcm word problems ?

The answer  for the question "How to solve hcf and lcm word problems ?" is purely depending upon the question that we have in the topic "H.C.F and L.C.M". The techniques and methods we apply to solve word problems on hcf and lcm  will vary from problem to problem.

The techniques and methods we apply to solve a particular  word problem  will not work for another word problem on HCF and LCM.

Even though we have different techniques to solve word problems in different topics of math, let us see the steps which are most commonly involved in "How to solve hcf and lcm word problems"

## Steps involved in solving HCF and LCM word  problems

To get answer for the question "How to solve hcf and lcm word problems? ", let us look at the steps involved in solving the word problem given below in the topic "H.C.F and L.C.M".

Problem:

The traffic lights at three different road crossings change after every 48 sec, 72 sec and 108 sec respectively. If they all change simultaneously at 8:20:00 hrs, when will they again change simultaneously?

Solution:

Step 1:

Let us understand the given information. There are four information given in the question.

1. There are three different  traffic lights

2. The first light changes every 48 seconds

3. The second light changes every 72 seconds

4. The third light changes every 102 seconds

Step 2:

Target of the question: If they all change simultaneously at 8:20:00 hrs, when will they again change simultaneously?

Step 3:

For example, let the two signals change after every 3 secs and 4 secs respectively.

Then the first signal changes after 3, 6, 9, 12 seconds...

Like this, the second signal changes after 4, 8, 12 seconds...

So, if the two signals change simultaneously now, again they will change simultaneously after 12 seconds.

This 12 seconds is nothing but the L.C.M of 3 seconds and 4 seconds

Step 4:

The same thing happened in our problem.

To find the time, when they will all change simultaneously, we have to find the L.C.M of (48,72,108).

L.C.M of (48,72,108) is 432 seconds = 7 min 12 sec

So, after every 7 min 12 sec, all the signals will change simultaneously.

Step 5:

At 8:20:00 hrs, if all the three signals change simultaneously, again they will change simultaneously after 7 min 12 sec.

That is at 8:27:12 hrs.

Hence, three signals will change simultaneously at 8:27:12 seconds.

Please click the below links to know "How to solve word problems in each of the given topics"

1. Solving Word Problems on Simple Equations

2. Solving Word Problems on Simultaneous Equations

3. Solving Word Problems on Quadratic Equations

4. Solving Word Problems on Permutations and Combinations

5. Solving Word Problems on HCF and LCM

7. Solving Word Problems on Time and Work

8. Solving Word Problems on Trains

9. Solving Word Problems on Time and Work.

10. Solving Word Problems on Ages.

11.Solving Word Problems on Ratio and Proportion

12.Solving Word Problems on Allegation and Mixtures.

13. Solving Word Problems on Percentage

14. Solving Word Problems on Profit and Loss

15. Solving Word Problems Partnership

16. Solving Word Problems on Simple Interest

17. Solving Word Problems on Compound Interest

18. Solving Word Problems on Calendar

19. Solving Word Problems on Clock

20. Solving Word Problems on Pipes and Cisterns

21. Solving Word Problems on Modular Arithmetic