Question

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together? [4 MARKS]

Answer 1

Concept: 1 Mark
Steps: 2 Marks
Solution: 1 Mark

The given numbers are 2,4,6,8,10 and 12.
The factors of the given numbers are:
2=1$\times$2
2=2$\times$2
6=2$\times$3
8=2$\times$2$\times$2
10=2$\times$5
12=2$\times$2$\times$3
Now ,the maximum number of times prime factor 2 occurs is 3,
the maximum number of times prime factor 3 occurs is 1,
the maximum number of times prime factor 5 occurs is 1.
So, LCM=2$\times$2$\times$2$\times$3$\times$5 = 120
L.C.M. of 2, 4, 6, 8, 10 and 12 is 120.
So, the bells will toll together after every 120 seconds (2 minutes).
In 30 minutes, they will toll together $\frac{30}{2}$ + 1 = 16 times.