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LOWEST COMMON FACTOR GRADE 6
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A school has two bells that ring at regular intervals. The first bell rings every 15 minutes, and the second bell rings every 20 minutes. At what time will both bells ring together?
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Find the LCM of 6 and 8.
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What is the LCM of 9, 12, and 15?
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1 Reply
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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
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