- The product of the two numbers is always equal to the product of their HCF and LCM.
- In case of HCF, if some remainders are given, then firstly those remainders are subtracted from the numbers given and then their HCF is calculated.
- In case of LCM, if a single remainder is given, then firstly the LCM is calculated and then that single reminder is added in that.
- In case of LCM, if for different numbers different remainders are given, then the difference between the number and its respective remainder will be equal. In that case, firstly the LCM is calculated, then that common difference between the number and its respective remainder is subtracted from that.
- Sometimes in case of HCF questions, the required remainder is given and when the remainder is not given, in those cases you will generally have three numbers given. For answering the question, you need to take the difference of the three pairs of numbers, now the HCF of these differences will become the answer e.g. if you have to find the greatest number, which when divides 83, 93 and 113 and leaves the same remainder. Here you will take the three differences i.e. 93 – 83 = 10 ; 113 – 93 = 20 ; 113 – 83 = 30, after that find the HCF of these differences, which comes out to be 10. Now you can check for yourself- when 10 divides these three numbers, the reminder obtained is 3 in each case and that is what the question was asking for.
- Whenever the question talks about the greatest or maximum, then in most of these cases it will be a question of HCF. Secondly, whenever the question is related to classification or distribution into groups, then in all the cases it is HCF only.
- Whenever the question talks about the smallest or minimum, then in most of the cases it will be a question of LCM. Secondly, whenever the word ‘together’ or ‘simultaneous’ is used in the question, then in all the cases it is LCM.
- Before solving the problems on HCF and LCM in the real exam, you must practice some HCF and LCM worksheets.

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Sometimes in such questions, the common remainder can also be asked. You can divide any of the numbers given by HCF (41 ¸ 10) and find the remainder to be equal to 1.

L.C.M. of 2/5, 3/10 and 6/25 = L.C.M of 2,3 and 6 / H.C.F of 5,10 and 25

L.C.M. of 2, 3 and 6 = 6 ; H.C.F. of 5, 10 and 25 = 5. Thus, the LCM of these three fractions will be 6/5.

⇒ Sometimes the question is how many times they toll together in the first hour, in that case after finding the answer like above, you need to add 1 for the start together as well i.e. in the first hour it is 1 more than the usual number of times.