Question

Light A flashes every 5 seconds.
Light B flashes every 6 seconds.
Light C flashes every 7 seconds.
All three lights flash at the same time.
Work out how long it will take for all three lights to flash at the same
time again​

Answer 1

Step-by-step explanation:

We have to find LCM of 5,6 and7

Answer 2

Answer:

It will take 3 minutes 30 seconds for all three lights to flash at the same time again.

Step-by-step explanation:

The light A flashes at 5 s, 10 s, 15 s, … In other words, multiples of five seconds.

The light B flashes at 6 s, 12 s, 18 s, … In other words, multiples of six seconds.

The light C flashes at 7 s, 14 s, 21 s, … In other words, multiples of seven seconds.

So the times when the lights flash together are least common multiples of 5, 6 and 7 seconds

Least Common Multiple means LCM.

Now question is how can we find LCM?

2 and 4 are two numbers.

By prime factorisation,

$2 = 2 \\ 4 = 2 \times 2$

So least common multiples of 2 and 4 is

$(2 \times 2) = 4$

Therefore LCM of 2 and 4 is 4.

Here given three numbers are 5,6,7.

By prime factorisation,

$5 = 5 \\ 6 = 2 \times 3 \\ 7 = 7$

Least Common Multiple of 5,6,7 is

$(5 \times 2 \times 3 \times 7) = 210$

Therefore LCM of 5,6,7 is 210.

Now All together light flash after 210 sec

$= \frac{210}{60} \: min \\ = 3 \: min \: 30 \: sec$

Two more LCM related Maths:

https://brainly.in/question/20776338

https://brainly.in/question/13493748