Sunday, 2 November 2025

Exercise (2.4).4

(i) Determine [20, 265, 530].

(ii) Find $\frac{1}{20}+\frac{1}{265}+\frac{1}{530}$ by using the result of (i).


(i) The prime decompositions are as follows.

$20 = 2^2 \times 5^1$

$265 = 5^1 \times 53^1$

$530 = 2^1 \times 5^1 \times 53*1$

The LCD $[20, 265, 530] = 2^2 \times 5^1 \times 53^1 = 1060$.


(ii) We use the LCD as the denominator for the fractions.

$$ \frac{1}{20}+\frac{1}{265}+\frac{1}{530} = \frac{53}{1060} + \frac{4}{1060} + \frac{2}{1060} = \frac{59}{1060}$$