Consider the following problem:
1. Swamy is having music classes on every fifth day and foot blass classes on every third day.
Today he attended both the classes. Then when will be the next day on which swamy is having both the classes?
In the above question, observe the words, every fifth, every third and both.
These are key words to identify that we need to find LCM of 5 and 3.
In general, you may find the words, least, minimum, etc. and conclude that the problem is to find LCM.
2. In a birthday party, the host decides to give some return gift bags to the guests. He decided to distribute 36 show pieces and 48 PET bottles wrapped in gift bags such that all the gift bags are identical (with equal numbher of show piece and petbottles) without leaving any gifts left over. Find the greatest (maximum) number of gift bags that the host can make?
Here you will be finding the HCF of 36 and 48 which is 12. So he can make a maximum (greatest) of 12 gift bags.
So greatest, maximum, all, identical are key words to conclude that the problem is to find HCF.