Page 8 - 9 Math 6

6. Algebraic Manipulation eLearn.Punjab

6.1.4 Application of H.C.F. and L.C.M.

Example
The sum of two numbers is 120 and their H.C.F. is 12. Find the
numbers.

Solution

Let the numbers be 12x and 12y, where x, y are numbers prime

to each other.

Then 12x + 12y = 120
i.e., x + y = 10

Thus we have to find two numbers whose sum is 10. The possible

such pairs of numbers are (1, 9), (2, 8), (3, 7), (4, 6), (5, 5)

The pairs of numbers which are prime to each other are (1, 9) and

(3, 7)

Thus the required numbers are

1 # 12, 9 # 12; 3 # 12, 7 # 12

i.e., 12, 108 and 36, 84.

EXERCISE 6.1

1. Find the H.C.F. of the following expressions.

(i) 39x7y3z and 91x5y6z7 (ii) 102xy2z, 85x2yz and 187xyz2

2. Find the H.C.F. of the following expressions by factorization.

(i) x2 + 5x + 6, x2 – 4x – 12

(ii) x3 – 27, x2 + 6x – 27, 2x2 – 18

(iii) x3 – 2x2 + x, x2 + 2x – 3, x2 + 3x – 4

(iv) 18(x3 – 9x2 + 8x), 24(x2 – 3x + 2)

(v) 36(3x4 + 5x3 – 2x2), 54(27x4 – x)

3. Find the H.C.F. of the following by division method.

(i) x3 + 3x2 – 16x + 12, x3 + x2 – 10x + 8

(ii) x4 + x3 – 2x2 + x – 3, 5x3 + 3x2 – 17x + 6

(iii) 2x5 – 4x4 – 6x, x5 + x4 – 3x3 – 3x2

4. Find the L.C.M. of the following expressions.

Version: 1.1 (i) 39x7y3z and 91x5y6z7 (ii) 102xy2z, 85x2yz and 187xyz2

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