LCM and HCF Problems Tips and Tricks

First learn the the formulas and how to find LCM and HCF on this page here.

Sum of two numbers is given and LCM and HCF is given. Find sum of reciprocals

Way to solve Type 1 Questions

Let numbers be a and b. So a + b is given. 

You know LCM x HCF = product of two numbers i.e. a x b is also given

So 1/a + 1/b = (a + b)/(a x b)

Example. If the sum of two numbers is 55 and the H.C.F. and L.C.M of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to

with this direct formula answer is 55/(5×120) = 11/120

Now this question can be iterated. Where some times LCM, product and sum is given but not HCF or other permutations of the same.

Biggest container to measure quantities

In this problem 3 quantities(containers) will be given you have to find a smaller quantity(container) that can measure those three quantities exactly

Way to solve type 2 Question

This is very easy, you just have to find the HCF of three quantities in such type of problems

Example.  Three different containers contain 496 litres, 403 litres and 713 litres of mixtures of milk and water respectively. What biggest measure can measure all the different quantities exactly

HCF of three numbers – 31 Lit.

Don’t know how to find HCF visit this page here.

Some times there is confusion whether to find LCM or HCF for a particular question.

Remember this rule of thumb then –

  • If outcome value is smaller than the inputs then HCF is to be found out e.g. in this question
  • If outcome value is larger than the inputs then LCM. e.g Type 3 problems

Bell Question – When will all clock Bell ring together

Way to solve Type 3 Question

Change bell timing into minutes or seconds and find the LCM of all of them

Example. Four different electronic devices make a beep after every 30 minutes, 1 hour, 3/2 hour and 1 hour 45 minutes respectively. All the devices beeped together at 12 noon. They will again beep together at:

  • Device A: 30 mins
  • Device B: 60 mins
  • Device C: 90 mins
  • Device D: 105 mins

So L.C.M of above devices is 1260 mins = 21 hrs.

That means they will make a beep together again after 21 hrs to 12 Noon, that is 9:00 am (12 noon + (12 + 9) = 9 am ) of next day…

Circle based Runner Problem

Way to Solve Type 4 Questions

Find LCM of all three times

Example. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point

L.C.M. of 252, 308 and 198 = 2772.

So, A, B and C will again meet at the starting point in 2772 sec. i.e., 46 min. 12 sec.

Some people in the comments have mentioned confusion about converting 2772 into mins.

  • 2772/60 = 46.2 now .2 in seconds will be .2×60 = 12 seconds so 46 mins and 12 seconds.
  • 46 mins 20 seconds is wrong as 46×60 = 2760! Now you say it’s 20 right, 2760+20=2780 ! Where 2760+12 = 2772 which is the answer

Basic approach to solve this should be

  • Divide Total number of seconds by 60, that is the minute part
  • Multiply the decimal part with 60 to get seconds as we have done in above example.