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Published on December 17th, 2010 In category Education | Maths

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# Concepts of HCF and LCM

Many times in examination the questions such as Find the greatest number that will divide exactly or smallest number which is exactly divisible by numbers such as 24, 12, 60 and 56  etc. Such question involve the concept of HCF and LCM.

So what is HCF and LCM and How do one answers to these questions… Take a look into the following

HCF : Highest common factor of two or more than two numbers is the greatest number that divides each of them exactly (without remainder). e.g., Consider the numbers 18, 24 and 36.

Find HCF of 18, 20 and 36

18 = 2 × 32
20 = 22 × 52
36 = 22 × 32 Therefore HCF = 2

LCM : The smallest number divisible by all the numbers is the Least Common Multiple of the given numbers.

What is the LCM of 16, 22 and 14?

16 = 24, 22 = 2 × 11, 14 = 2 × 7
LCM = 16 × 11 × 7 = 1232

IMPORTANT CONCEPT : Product of numbers  =  HCF x LCM of the numbers

Also if The HCF and LCM of two nos. are equal when they are equal.