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?

# Three alarm clocks ring at intervals of 4, 12 and 20 minutes respectively. If they

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Answer:## Given :-

## To Find :-

## Solution :-

[tex]\mapsto[/tex] Three alarm clocks ring at intervals ofandminutes respectively.

4,1220Since,sowehavetofindtheirL.C.M:[tex]\bigstar[/tex]

4[tex]\implies \sf 2 \times 2[/tex]

[tex]\bigstar[/tex]

12[tex]\implies\sf 2 \times 2 \times 3[/tex]

[tex]\bigstar[/tex]

20[tex]\implies\sf 2 \times 2 \times 5[/tex]

[tex]\longmapsto[/tex]

L.C.Mof4,12and20are:[tex]\implies \sf 2 \times 2 \times 3 \times 5[/tex]

[tex]\implies \sf 4 \times 15[/tex]

[tex]\implies \sf\boxed{\bold{\red{60}}}[/tex]

[tex]\therefore[/tex]

Thethreeclocksringtogetherafter60minutesor1hours.Given:–ToFind:–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

[tex]:\implies[/tex] 2 |

4,12,20[tex]:\implies[/tex] 2 |

2,6,10[tex]:\implies[/tex] 2|

1,3,5[tex]:\implies[/tex] LCM of 4 , 12 & 20 = 2 × 2 × 3 × 5

[tex]:\implies[/tex] LCM = 60

Hence,theywillringtogetherafter60minutes.