When you understand and use LCM in doing Math, it becomes a lot easier when doing certain calculations and certain problem sums. LCM refers to Lowest Common Multiples.
Examples:
The LCM of 2 and 5 is 10.
The multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 ...
The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60 ...
The common multiples of 2 and 5 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120 ...
The LCM of 2 and 5 is 10.
Important note:
Once we've found the LCM, we can find the other common multiples easily since they are all multiples of the LCM.
So, if we want to find the seventh common multiple of 2 and 5, we simply multiple the LCM by 7.
Examples of Questions where we can use LCM to find the answer quickly:
Qn: What is the fifth common multiple of 3 and 4?
Ans: LCM of 3 and 4 is 12. The fifth common multiple of 3 and 4 is 5 x 12 = 50
Qn: Write down the tenth common multiple of 6 and 9.
Ans: LCM of 6 and 9 is 18. The tenth common multiple of 6 and 9 is 10 x 18 = 180
Qn: Find the twentieth common multiple of 4 and 10.
Ans: LCM of 4 and 10 is 20. The twentieth common multiple of 4 and 10 is 20 x 20 = 400
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How to find LCM
There are 3 kinds of LCM:
1) When there is no common factor, the LCM is simply the product of the given numbers
Examples:
The LCM of 3 and 5 is 3 x 5 = 15
The LCM of 4 and 7 is 4 x 7 = 28
The LCM of 5 and 12 is 5 x 12 = 60
2) When one given number is a factor of the other number, the LCM is the larger number
Examples:
The LCM of 3 and 6 is 6
The LCM of 3 and 12 is 12
The LCM of 4 and 8 is 8
The LCM of 4 and 20 is 20
The LCM of 5 and 15 is 15
3) When there is a common factor, we need to take out the common factor or factors, and ... let's look at the examples
Examples:
The LCM of 4 and 6 is 12
The LCM of 6 and 10 is 30
The LCM of 8 and 20 is 40
The LCM of 9 and 15 is 45
