Finding Least Common Multiple of two or more numbers is a very basic step in several mathematical problems. The term itself is so clear that you do not need a definition for least common multiple of numbers.
Often I have noticed people using the regular division approach for finding LCM of two simple numbers like 12 and 24 for which LCM can be told almost instantly by looking at the numbers. So I would like to explain the shortcut method in this article.
1. First pick the biggest number.
2. Then check if each multiple of the bigger number is a multiple of the other number(s) as well. If so, you have found the LCM.
Since we need common multiple we are checking if the multiples of one number is the multiple of other numbers as well. Also we are starting from the minimum and checking each multiple of a number, so we can ensure that we don’t miss the “least” common multiple.
But why to choose the bigger number? We can get to the LCM quickly by listing the multiples of bigger number when compared to smaller number.
Example 1 – 12,24
In the example of 12 and 24, 24 itself is a multiple of 12. So 24 is the LCM.
Example 2 – 12,8
Pick 12. 12 is not a multiple of 8. 24 (12*2) is a multiple of 8. So LCM is 24
Example 3 – 5,10
Pick 10. 10 itself is a multiple of 5. So, LCM is 5.
Example 4 – 8,16,20
Pick 20. Multiples of 20 – 20,40,60 are not multiples of both 8 and 16. Next we have 80(20*4) which is divisible by both 8 and 16. So 80 is the LCM.
Example 5 -25,30
Pick 30. 30,60,90,120 are all not multiples of 25. 150 is. So 150 is the LCM.
Example 6 – 6,9,12
Pick 12. 12,24 are not multiples of both 6 and 9. But 36 is. So 36 is the LCM.
Example 7 -22,33
Pick 33. 33 is not a multiple of 22 but 66 is. 66 is the LCM
Example 8 – 12,17
You should start listing the factors of 17. If you find the shortcut being difficult at any point in time, just go to the usual method.
In this example, I would like to mention one more tip. If the given numbers are coprimes, just multiple them to get the LCM. Here,12*17 is 204. LCM is 204
Example 9 – 11,6
11 and 6 are coprimes as they don’t have any common factors. So 11*6 = 66 is the LCM.