Name: Basic Concepts of HCF and LCM
Uploaded: 2019-07-19
Duration: 5 min 39 s
Description: Maths is a subject you understand, not a subject you memorise. So learning the application of the concepts helps you fully understand the topic.

Question

Four bells ring at an interval of

45 \min, 1 hr, 1 hr 15 \min

and

1 hr 30 m .

Let's find bells ringing together at

12

, when will these ring together again. Also let's find, how many times the bells will separately ring during these hours.

Accepted Answer

Given,

Four bells ring at an interval of $45 \min, 1 hr, 1 hr 15 \min & 1 hr 30 \min$ . To find out at what time the bells ring together we need to find the L.C.M.

The first bell ring at $45 \min$

The second bell ring at $1 hr$ i.e., $1 hr = 60 \min$

The third bell ring at $1 hr 15 \min = 60 \min + 15 \min = 75 \min$

The fourth bell ring at $1 hr 30 \min = 60 \min + 30 \min = 90 \min$

Now, to find the $L . C . M (45, 60, 75, 90)$

$\begin{matrix} 5 & 45 & 60 & 75 & 90 \\ 3 & 9 & 12 & 15 & 18 \\ 3 & 3 & 4 & 5 & 6 \\ 2 & 1 & 4 & 5 & 2 \\ 1 & 2 & 5 & 1 \end{matrix}$

Therefore, the $L . C . M (45, 60, 75, 90)$ is $3 \times 3 \times 5 \times 5 \times 2 \times 2 = 900$ .

Now, converting into hours $\frac{900}{60} = 15 hrs$ .

The four bells ring together at $3 (or) 15 hrs$ .

Now, the first bell will ring $\frac{900}{45} = 20$ times

The second bell will ring $\frac{900}{60} = 15$ times

The third bell will ring $\frac{900}{75} = 12$ times

The fourth bell will ring $\frac{900}{90} = 10$ times

West Bengal Board Solutions for Chapter: Hcf and Lcm of Three Numbers, Exercise 4: Let do ourselves - 12.2

West Bengal Board Mathematics Solutions for Exercise - West Bengal Board Solutions for Chapter: Hcf and Lcm of Three Numbers, Exercise 4: Let do ourselves - 12.2

Questions from West Bengal Board Solutions for Chapter: Hcf and Lcm of Three Numbers, Exercise 4: Let do ourselves - 12.2 with Hints & Solutions

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