Question

Q.2 Three bells toll at intervals of 9, 12 and
is minutes of they start tolling together,
after what time they will next tale
together?
ans​

Answer 1

$\large\underline{\text{Answer}}$

36 minutes

$\large\underline{\text{Main idea}}$

A bell tolls every 9 minutes, so if time is a multiple of 9 minutes, the bell tolls.

It is the same for the other bell that tolls when time is a multiple of 12 minutes.

$\large\underline{\text{Explanation}}$

For two bells to toll together, the time should be both multiples of 9 minutes and 12 minutes. Such the smallest number is called the LCM.

Finding the LCM

$\boxed{ \begin{aligned} &(1)\ 9= \underline{3^{2}}\\&(2)\ 12= \underline{2^{2}} \times 3 \end{aligned} }$

When we find the LCM, we find the highest power of each prime and multiply them all together. The lowest common multiple of time is $\text{ 2^{2} \times 3^{2}=36 minutes.}$

Hence, the bells toll together after 36 minutes.

Answer 2

$\large \underline{ \underline \text{Appropriate Question:}}$

• Two bells toll at intervals of 9 and 12 is minutes of they start tolling together, after what time they will next tale together?

$\large \underline{ \underline \text{Solution:}}$

As given,

• The Bell 1 bells at the interval of 9min.

And,

• The Bell 2 bells at the interval of 12min.

To find,

• At what time they will tale together?

To find this,

• We have to find out the LCM of 9 and 12.

Let us find the LCM by prime factorisation method,

• Prime factorisation of 9 = 3 × 3 × 1

And,

• Prime factorisation of 12 = 2 × 2 × 1

Here,

• The Prime factorisation of 9 = 3² × 1

And,

• The Prime factorisation of 12 = 2² × 3 × 1

So,

• ➺ LCM (9,12) = 2² × 3²

• ➺ LCM (9,12) = 4 × 9

• ➺ LCM (9,12) = 36

Hence,

• The LCM of 9 and 12 is 36.

Therefore,

• The Bells will tale together at 36th minutes.

.

$\large \underline{ \underline \text{Required Answer:}}$

• The Bells will tale together at 36th minutes.