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Solution 1-

Step 1: Given – The first Bell rings every 15 minutes and the second Bell rings every 20 minutes.

To find – At what time will both Bell will ring together

Concept – so basically here we have to find LCM of 15 and 20 and that will be the time both Bell will ring together.

Step 2 :

List the prime factors of each:

15:5 x 3

20:2 X 2 X 5

Step 3: Multiply each factor the maximum number of times it occurs in any of the numbers.

The occurrence of Numbers in the above example:

5 – one time

3 – one time

2 – two time

So 5 X 3 X 2 X 2 = 60

This gives us 60, the lowest number that can be divided evenly by 15 and 20.

Hence the bell will ring together after 60 minutes.

Solution 2:

Step 1:

We are given two numbers 6 and 8

To find: LCM of two numbers 6 and 8

Step 2:

List the prime factors of each:

6:2X3

8:2X2X2

Step 3: Multiply each factor the maximum number of times it occurs in any of the numbers.

The occurrence of Numbers in the above example:

2: three times

3: one time

So LCM of 6 and 8 will be 2X2X2X3= 24

Solution 3:

Step 1:

We are given three numbers 9,12and 15

To find: LCM of three numbers 12,9 and 15

Step 2:

List the prime factors of each:

9: 3X3

12:2X2X3

15:3X5

Step 3: Multiply each factor the maximum number of times it occurs in any of the numbers.

The occurrence of Numbers in the above example:

3- two times

2: two times

5: one times

So LCM will be 3X3X2X2X5=180