Question

Three alarm clocks ring at intervals of 4, 12 and 20 minutes respectively. If they
start ringing together, after how much time will they next ring together?

Answer 1

Given:-

• Three alarm ring at intervals of 4, 12 & 20 minutes .

To Find:-

• How much time will they ring together ?

Solution:-

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀According to the Question

It is given that three alarm ring at intervals of 4, 14 & 20 minutes. We need to calculate when they will ring together ? .So, they will ring together, the LCM (Lowest Common Multiple) of given time interval .

Now, Finding the LCM of 4, 12 , 20

$:\implies$ 2 |4 , 12 , 20

$:\implies$ 2 |2 , 6 , 10

$:\implies$ 2|1 , 3 ,5

$:\implies$ LCM of 4 , 12 & 20 = 2 × 2 × 3 × 5

$:\implies$ LCM = 60

• Hence, they will ring together after 60 minutes .

Answer 2

Answer:

Given :-

• Three alarm clocks ring at intervals of 4 , 12 and 20 minutes respectively.
• They start ringing together.

To Find :-

• How much time will they next ring together.

Solution :-

$\mapsto$ Three alarm clocks ring at intervals of 4 , 12 and 20 minutes respectively.

Since, all the three clocks ring together, so we have to find their L.C.M :

$\bigstar$ 4

$\implies \sf 2 \times 2$

$\bigstar$ 12

$\implies\sf 2 \times 2 \times 3$

$\bigstar$ 20

$\implies\sf 2 \times 2 \times 5$

$\longmapsto$ L.C.M of 4 , 12 and 20 are :

$\implies \sf 2 \times 2 \times 3 \times 5$

$\implies \sf 4 \times 15$

$\implies \sf\boxed{\bold{\red{60}}}$

$\therefore$ The three clocks ring together after 60 minutes or 1 hours.