HCF is the highest number that is the greatest thing for simplifying fractions.The smallest positive number that the multiple of two or more numbers is LCM.
source: www.cbsetuts.com Fig: Highest Common Factor
HCF is the highest number that is the greatest thing for simplifying fractions. For example, the factors common to 12 and 3 are 2,3.
\(\therefore\) HCF of 12 and 8 is 3.
HCF of monomial expressions We can find the HCF of the given monomial expressions just by taking the common variable with the least power. The HCF of the numerical coefficient is obtained as like in the case of arithmetic. For example, Find the HCF of x4y2 and x2y4 1st expression = x4y2 2nd expression = x2y4 \(\therefore\) HCF = x2y2
HCF of polynomial Expression We can find the HCF of polynomials by factorizing them. For example, Find HCF of ax - bx and a2 - b2 1st expression = ax - bx= x(a-b) 2nd expression = a2 - b2 = (a-b)(a+b) \(\therefore\) = (a-b)
Lowest Common Multiple (LCM)
source: www.cbsetuts.com Fig: Lowest Common Multiple
The smallest positive number that the multiple of two or more numbers is LCM. For example, the LCM of a2 and a3 is a3.
Lowest common factor of monomial expressions We can find the LCM of the given monomial expressions just by taking the common variable with the highest power. For examples, 1sr expression = ax2 2nd expression = a2x2 \(\therefore\) a2x2
LCM of polynomial expressions To find LCM of polynomial expressions . We should factorize them. Then the product of a common factors and remaining factors is the LCM of the given expressions. For examples, Find the L.C.M of ax2 + ax and a2x2 + a2x 1st expression = ax2 + ax = ax(x+1) 2nd expression = a2x2 + a2x = a2x(x+1) \(\therefore\) LCM = a2x(x+1)
Things to remember
We can find the HCF of the given monomial expressions just by taking the common variable with the least power.
We can find the HCF of polynomials by factorizing them.
We can find the LCM of the given monomial expressions just by taking the common variable with the highest power.
To find LCM of polynomial expressions . We should factorize them. Then the product of a common factors and remaining factors is the LCM of the given expressions.
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It is a network of social relationships which cannot see or touched.
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