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H.C.F and L.C.M Concept

Posted by Ravi Kumar at Thursday, August 4, 2011
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Facts And Formulae:

Highest Common Factor:(H.C.F) or Greatest Common Measure(G.C.M) :
The H.C.F of two or more than two numbers is the greatest number that divides each of them exactly.

There are two methods :

i.Factorization method: Express each one of the given numbers as the product of prime factors. The product of least powers of common prime factors gives HCF.

Example : Find HCF of 26 * 32*5*74 , 22 *35*52 * 76 ,
2*52 *72
Solution: The prime numbers given common numbers are 2,5,7
Therefore HCF is 22 * 5 *72 .

ii.Division Method : Divide the larger number by smaller one. Now divide the divisor by remainder. Repeat the process of dividing preceding number last obtained till zero is obtained as number. The last divisor is HCF.

Least common multiple[LCM] : The least number which is divisible by each one of given numbers is LCM.

There are two methods for this:
i.Factorization method : Resolve each one into product of prime factors. Then LCM is product of highest powers of all factors.

ii.Common division method.

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