The first bell rings every 20 minutes, second bell rings every 30 minutes, and the third bell rings every 50 minutes. If all three bells ring the same time at 12:00pm, when will be the next time the three bells will ring together?

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vhudzeniy2n · Accepted Answer

Step 1  So first you find the LCM, or least common multiple, (can be called LCD, least common denominator).  The LCM of 20, 30, and 50 is basically  10×2×3×5  because you factor out the 10 since that is a common factor.  10×2×3×5=300  This is the number of minutes. To find the number of hours, you simply divide by 60 and get 5 hours. Then you count 5 more hours from 12:00 pm and get 5:00 pm.

falwennaf5c7 · Accepted Answer

Step 1Expanding on Ayushi&#039;s answer.Notice that we have:10×210×310×5Each of 2, 3 and 5 are &#039; numbers. So the only common values they will divide exactly into is their product or some multiple of that productSo for 2,3 and 5 the least positive value they will divide into is:2×3×5=30but each of 2,3,and 5 is multiplied by 10 so we have to also multiply their product by 10 giving:10×30=300Step 2A different line of thinking that ends up in the same place3 and 5 are odd numbers but 2 is even.As 2 is even then the target value has to also be even. Otherwise 2 will not divide exactly into itBut some form of 3 and 5 have to be able to divide exactly into this even number as well.3×5=15which is not even. However if we multiply 15 by 2 then 2 is automatically a factor:2×15=2×3×5=30← even numberHowever we are counting in tens. In that we have 2 tens, 3 tens and 5 tens. So the answer is also counting in tens. Thus we have 30 tens =300 in minutes1200 hours+30060=1200 hours+5 hours=1700 hoursAlternatively written as 5 pm

The first bell rings every 20 minutes, second bell rings

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