HCF and LCM Using Prime Factorisation


 
 
Concept Explanation
 

HCF and LCM Using Prime Factorisation

HCF and LCM Using Prime Factorisation:

Let a and b be two non-negative integers, not both zero. We denote the highest common factor (HCF) and least common multiple (LCM) of a and b by HCF(a,b) and LCM(a,b), respectively.

HCF(a,b) = Product of the smallest power of each common prime factor in the numbers.

LCM (a,b) = Product of the greatest power of each common prime factor in the numbers.

Example: Find the LCM and HCF of 6 and 20 by the prime factorisation method.

 6 = 2 X 3

20= 2 X 2 X 5

HCF (6,20) = 2 as 2 is the only common factor of 6 and 20

LCM (6, 20) = 2 X 2 X 3 X 5= 60

From the above relation we can state that

HCF(a,b) X LCM(a,b) = a X b

Sample Questions
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Question : 1

The L.C.M. OF 119 and 343 is  ________________

Right Option : D
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Explanation
Question : 2

The L.C.M. of 44 and 90 is ______________

Right Option : B
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Explanation
Question : 3

Find the HCF of 410 and 96.

Right Option : A
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Explanation
 
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