Three bells ring at intervals of 30 minutes, 40 minutes and 60 minutes for lower, middle and upper primary respectively. If they all ring together at 8:30am; a) After how long will they ring together again?

$$30 = 2 \times 3 \times 5$$ $$40 = 2^3 \times 5$$ $$60 = 2^2 \times 3 \times 5$$

$$LCM(30, 40, 60) = 2^3 \times 3^1 \times 5^1 = 8 \times 3 \times 5 = 120$$

The bells will ring together again after 120 minutes.

b) To find the exact time they will ring together again, we convert the minutes to hours and add it to the initial time.

$$8:30 \text{ am} + 2 \text{ hours} = 10:30 \text{ am}$$

The bells will ring together again at 10:30 am.

a) The bells will ring together again after $\boxed{\text{120 minutes}}$.

b) The bells will ring together again at $\boxed{\text{10:30 am}}$.