# Three alarm clocks ring at intervals of 4, 12 and 20 minutes respectively. If they start ringing together, after how much t

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?

### 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.

2. 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 .