how can we determine whether to use hcf or lcm in a given word problem
Answers
Avoid the term “TRICK” like the plague. It is misleading and is used by very many coaching institutes to lure gullible students to them. There is nothing called TRICK or SHORTCUT in mathematics.
Having said that, let us talk about the problem at hand. It is very easy if we know the meaning of LCM and HCF.
Least Common Multiple, also called LCM is that smallest number which is completely divisible by a given set of numbers. For example, 30 is completely divisible by 5, 10 & 15 and hence is the LCM of 5,10 & 15. There is no number less than 30 that can boast the same.
So, whenever you are required to find a number that is divisible by more than one number, you have to find LCM.
Highest Common Factor, also called HCF, is that highest number that completely divides a given set of number. For example, 25 divides 50, 75, 100, 125, 725, 950. Since there is NO number greater than 25 that divides the given set of numbers, we call 25 as the Highest Common Factor or HCF.
So, whenever you are required to find a number that completely divides more than one number, you have to find HCF.