Finding the Least Common Multiple: Lesson Topic Index | Grade 7 Math | Intermediate Test Prep | StudyZone

 In this lesson we will learn how to find the LCM or Least Common Multiple of 2 or more numbers

 The Least Common Multiple (LCM) is the smallest number that two or more numbers will divide into evenly. To find the multiples of a number simply multiply the number by every whole number. For example, to find the multiples of 4 we follow this pattern 0 (4x0), 4 (4x1), 8 (4x2), 12 (4x3), 16 (4x4) ... To find the multiples of 8: 0 (8x0), 8 (8x1), 16 (8x2), 24 (8x3) 32 (8x4)... When we are asked for a set of multiples we just list them like this. M7 = 0,7, 17, 21, 28, 35, 42, 49, ...

 Let's look at the set of multiples for the two numbers 4 and 6 M4 = 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 ... M6 = 0, 6, 12, 18, 24, 30, 36, 42 ...

Did you notice that 0, 12, 24 and 36 were in both lists?
We call these common multiples.

The smallest non-zero common multiple is called the "Least Common Multiple"

So the LCM for 4 and 6 is 12.

Let's look at another example.

 Find the LCM for 12 and 16 First list the multiples of both numbers. M12 = 0, 12, 24, 36, 48, 60, 72, 84, 96 ... M16 = 0, 16, 32, 48, 64, 80, 96 ... The smallest non-zero common multiple is 48. Therefore the LCM for 12 and 16 is 48.

The number of multiples in your list depends on the number being used. The LCM is usually within the first 10 multiples. If it doesn't appear by then just keep adding multiples until one appears on both lists.
Now, let's get serious!

 Find the LCM for 9, 12 and 36 M9 = 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 ... M12 = M36 =

During the month Sheila put money into her account and took money out.  You have to figure how much money she had at the beginning of the month

To do that, start with the ending balance and work backwards, using inverse operations.

 Start with ending balance Add back \$14 check charge   Add back \$617 check   Add back \$98 check   Subtract \$385 deposit \$899 +  14   913 +617 1530 +  98 1628 -385 \$1249   balance at end of May

Let's try some on your own!