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Dividend, Divisor, Quotient, Remainder

Find the L.C....

Question

Find the L.C.M. of the following expressions by division method.

a³ − 3a² − 10a + 24 and a³ − 2a² − 9a + 18

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Solution

The given expressions areand
We use the division method to find the H.C.F. of the given expressions.
We know that
Hence, the L.C.M. of the given expressions is.

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\frac{a^{2} - 16}{a^{3} - 8} \times \frac{2 a^{2} - 3 a - 2}{2 a^{2} + 9 a + 4} \div \frac{3 a^{2} - 11 a - 4}{a^{2} + 2 a + 4}

Q. Find the L.C.M. of the two expressions

a^{2} + 7 a - 18

a^{2} + 10 a + 9

with the help of their H.C.F.

Q. Find the H.C.F. of

(a^{3} + 4 a^{2} + 4 a + 1)

(a^{4} + 3 a^{3} + 2 a^{2} + 3 a + 1)

by using the division method.

Q. Find the GCD of

(a^{3} - 4 a^{2} + 7 a - 6)

(a^{3} - 5 a^{2} + 10 a - 8)

by using the division method.

3

8 + 13 a + 7 a^{2} .

Two of them are

2 a^{2} + 3 a + 2

3 a^{2} - 4 a + 1

. Find the third expression.

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