The fol lowing is an alternative method for determining the Least Common
Multiple of a set of numbers. Students usually find
this method easy to learn and use, especially when studying the Least Common
Denominator ( LCD ) needed for the second
test.
Example 1: Find the LCM for 6, 3 and 16
Since there is no prime number that divides at least two of the bottom
numbers, we are finished.
The LCM is the product of the outside numbers: 2 x 3 x 1 x 1 x 8 = 48
RULE : To de termine the Least Common Multiple (LCM):
1. Write the numbers in a horizontal line.
2. Divide by the smallest prime number that divides at least two of the
numbers. Bring down any number(s)
that cannot be divided evenly.
3. Repeat the second step until no prime number will evenly divide at
least two of the bottom numbers. |
Example 2: Find the LCM of 3, 18, 9 and 4
The smallest prime that
divides at least two of
them is 2.
Here, 3 is the smallest.
Here again, 3 is the smallest.
At this point, there is no prime that divides at least two of the bottom
numbers--so we are finished.
The LCM is the product of the outside numbers: 2 x 3 x 3 x 1 x 1 x 1 x 2 = 36
Example 3: Find the LCM of 7 and 5
No prime number divides 7 and 5 evenly; therefore, the LCM is
7 * 5 = 35
Example 4: Find the LCM of 6 and 9
The LCM is 3 * 2 * 3 = 18
Example 5: Find the LCM of 12, 15 and 24
The LCM is 2 * 2 * 3 * 1 * 5 * 2 = 120
Example 6: Find the LCM of 4, 12 and 18
The LCM is 2 * 2 * 3 * 1 * 1 * 3 = 36
| SELF-TEST |
| Use the Horizontal-Line Method to find the Least Common
Multiple (LCM) of the following: |
1) 6, 18
2) 3, 5, 6
3) 3, 5, 7
4) 24, 36, 40
5) 12, 42, 39
6) 17, 51, 68, 12 |
ANSWERS
1) 18 2) 30 3) 105
4) 360 5) 1092 6) 204 |
