Question

1.Four bells are heard at intervals of 6, 8, 12 and 18 seconds respectively since 12 o’clock. How many times can they be heard simultaneously within 6 minutes of the time (excluding the one at the start)? *
1 point
(1) 6
(2) 5
(3)8
(4) 9

Answer 1

Answer hai (1) 6 Right answer

Step-by-step explanation:

1

Answer 2

The bell will ring 5 times in 6 minutes excluding the bell at the start.

Solution:

To calculate this sum we should take the Lowest Common Multiple (L.C.M) of 6,8,12 and 18.

Finding L.C.M:

Write numbers as multiplication of its prime factors

$6 \rightarrow 2 \times 3 \rightarrow 2 \text { comes once and } 3 \text { comes once }$

$8 \rightarrow 2 \times 2 \times 2 \rightarrow 2 \text { comes three times }$

$\begin{array}{l}{12 \rightarrow 2 \times 2 \times 3 \rightarrow 2 \text { comes twice and } 3 \text { once. }} \\ {18 \rightarrow 2 \times 3 \times 3 \rightarrow 2 \text { comes once and } 3 \text { twice }}\end{array}$

So maximum times is three times for 2 and two times for 3

Hence least common multiple is $=2 \times 2 \times 2 \times 3 \times 3=72$

So L.C.M of 6,8,12 and 18 is 72

So the bell rings simultaneously every 72 seconds.

In 72 second there is 1 bell

Therefore in 6 minutes i.e. 360 seconds there will be $\frac{360}{72}$ = 5 bell.

Excluding the bell at the start which rung at 12 O’ clock, the bell will ring 5 times in 6 minutes.