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Saturday, October 13, 2012

Least Common Multiple, LCM

Category: Arithmetic

"Published in Newark, California, USA"

What is the Least Common Multiple (LCM) for the following numbers: 24, 36, 18, and 12?

Solution:

There are two ways in getting their LCM. I will show the both methods and let's see which method is your preference.

Method 1: You can use the intersection method. You have to list the multiples of each given numbers.

A = (24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, 288...)
B = (36, 72, 108, 144, 180, 216, 252, 288, 324, 360, 396.......)
C = (18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216.....)
D = (12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228...)

If A ∩ B ∩ C ∩ D = (72, 144, 216,.......)

Therefore, their LCM is 72


Method 2: You can use the continuous division method. You have to think their factors as much as you can while dividing the numbers until the quotients are all equal to 1.

          6       24          36           18            12
             2      4            6             3              2
              2   │  2            3             3              1
               3   │ 1            3             3              1
                       1            1             1              1

Therefore, the LCM is 6 x 2 x 2 x 3 = 72.

Note: Please remember how to get the LCM of the numbers very well because you will use this method later in making dissimilar fractions into similar fractions. You can add or subtract fractions if they are similar fractions where their denominators are the same. If their denominators are different or the fractions are dissimilar, then you have to make the fractions into similar fractions first by getting the Least Common Multiples (LCM) of the denominators. Once the denominators are the same, then you can add or subtract the fractions. In solving fractions, usually LCM is called Least  Common Denominator (LCD). Still, I encourage you to memorize or remember the prime and composite numbers.