(i) Find [3, 4, 28].
(ii) Solve the following equation
$$ \frac{1}{3} + \frac{1}{4} + \frac{1}{28} + x = 1 $$
without using a calculator.
(i) The prime decompositions are as follows.
$3 = 3^1$
$4 = 2^2$
$28 = 2^2 \times 7^1$
And so the LCM $[3,4,28] = 2^2 \times 3^1 \times 7^1 = 84$
(ii) The fractions rewritten using the LCM as the denominator, gives
$$ \frac{28}{84} + \frac{21}{84} + \frac{3}{28} + x = 1 $$
That is,
$$ x = \frac{84}{84} - \frac{52}{84} = \frac{32}{84} = \frac{8}{21}$$