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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.
Lowest Common Multiple (LCM)
The smallest positive number that the multiple of two or more numbers is LCM. For example, the LCM of a^{2} and a^{3} is a^{3}.
Solution:
1st expression = x^{4}y^{2}
2nd expression = x^{2}y^{4}
\(\therefore\) HCF = x^{2}y^{2}
Solution:
1st expression = 4ab^{2}
= 2×2ab^{2}
2nd expression = 6a^{2}b^{3}
= 2×3a^{2}b^{3}
\(\therefore\) HCF = 2ab^{2}
Solution:
1st expression = ax - bx = x(a-b)
2nd expression = a^{2} -b^{2} = (a+b)(a-b)
\(\therefore\) HCF = (a-b)
Solution:
1st expression = x^{2} + xy + zx + yz = x(x+y) + z(x+y) = (x+y) (x+z)
2nd expression = x^{2} - y^{2} = (x+y) (x-y)
\(\therefore\) HCF = (x+y)
Solution:
1st expression = 4x^{3}y^{3}
= 2×2x^{3}y^{3}
2nd expression = 6xy
= 2×3xy
\(\therefore\) LCM = 2×2×3 x^{3}y^{3}
= 12x^{3}y^{3}
Solution:
1st expression = ax^{2} + ax = ax(x+1)
2nd expression = a^{2}x^{2} + a^{2}x = a^{2}x(x+1)
\(\therefore\) LCM = a^{2}x(x+1)
What is the H.C.F. of x^{4}y^{2 }and x^{2}y^{4}
What is the H.C.F. of 4ab^{2} and 6a^{2}b^{3}
Find the L.C.M. of ax^{2 }and a^{2}x^{2}
Find the L.C.M. of 4x^{3}y^{3} and 6xy
Find the L.C.M. of a^{2} + a and a^{2} - 1
Find the H.C.F of ax - bx and a^{2} - b^{2}
Find the H.C.F. of p^{4}q^{3} and p^{3}q^{4}
Find the L.C.M. of a^{2} and a^{3}
Find the L.C.M. of 2x + 4 and x^{2} + 2x
Find the H.C.F. of x^{3} - x^{2}y and x^{2} - y^{2}
Find the L.C.M. of a^{2} - 5a + 3ab - 15ab and ax - 5x
ASK ANY QUESTION ON Factorisation, HCF and LCM
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