# 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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5pm

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Notice that we have:

Each of 2, 3 and 5 are prime numbers. So the only common values they will divide exactly into is their product or some multiple of that product

So for 2,3 and 5 the least positive value they will divide into is:

but each of 2,3,and 5 is multiplied by 10 so we have to also multiply their product by 10 giving:

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3 and 5 are odd numbers but 2 is even.

As 2 is even then the

But some form of 3 and 5 have to be able to divide exactly into this even number as well.

However 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

Alternatively written as 5 pm

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So first you find the LCM, or least common multiple, (can be called LCD, least common denominator).

The LCM of

#10 * 2 * 3 * 5#

because you factor out the

#10 * 2 * 3 * 5 = 300#

This is the number of minutes. To find the number of hours, you simply divide by

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