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Subject – Mathematics

Chapter 3 – FACTORS AND MULTIPLES

Sub-topic-7:- Word problem on HCF and LCM

Solving word problem is a very important part of mathematics, because with them you understand
and practice what you have earned.

How will you know when to use LCM and HCF to solve word problem

Keywords for LCM

 Repetition
 Cycle
 Happen at same time again
 Smallest/least

Keyword for HCF

 Grouping

 Split/divide equally
 Share
 No leftovers
 Greatest /largest.
 maximum

For example:-

 Find the largest number that divides 92 and 74 leaving 2 as remainder.

The number divides 92 and leaves 2 as remainder

Therefore, the number divides 92 - 2 = 90 exactly

The number also divides 74 leaving 2 as remainder

Therefore, the number divides 74 - 2 = 72 exactly

Now we have to find highest common factor (H.C.F.) of 90 and 72

Highest common factor (H.C.F.) of 90 and 72 = 18

Therefore, 18 is the required number.

 Five bells begin to toll together and toll respectively at interval 6,7, 8 and12seconds .After
how much time will they toll together again?

Solution:- As the keyword together again is given then we have to find the LCM