SOLUTION: three bells ring at intervals of 7,10,14 minutes respectively.they begin by ringing together. after how long will they ring together again?

Question 186732: three bells ring at intervals of 7,10,14 minutes respectively.they begin by ringing together. after how long will they ring together again?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
You can answer this question by finding the Least Common Multiple (LCM) of the three numbers.
One approach is to find the prime factors of each of the numbers;
The prime factors are:
7 = 7
10 = 2*5
14 = 2*7
Now if any of the three numbers has repeating factors (there are none in this case) you would express those repeating factors in exponential form.
Now select the highest power of each factor (here, that's 2, 5, and 7) and multiply them.
2*5*7 = 70
LCM = 70
The bells will ring together again in 70 minutes (1 hour & 10 mins)
You could also list the multiples of each of the three numbers, then select the smallest common multiple from the three lists.
7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 77,...
10: 10, 20, 30, 40, 50, 60, 70, 80,...
14: 28, 42, 56, 70, 84,...
You can see that 70 is the smallest (least) common multiple.
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