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

2 thoughts on “Three alarm clocks ring at intervals of 4, 12 and 20 minutes respectively. If they <br /> start ringing together, after how much t”

1. 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 :-

   [tex]\mapsto[/tex] 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 :

   [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.M of 4 , 12 and 20 are :

   [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] The three clocks ring together after 60 minutes or 1 hours.

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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

   [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, they will ring together after 60 minutes .

   Reply