"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.

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"

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**

**6. Solving Word Problems on Numbers**

**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**

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