The least common multiple (LCM) is the least number that is a common multiple of two or more numbers. Suppose you want to find the LCM of 4, 6, and 9. Write multiples of each number until you find a common multiple.
multiples of 4: 0, 4,
8, 12, 16, 20, 24, 28, 32, 36, . . .
multiples of 6: 0, 6,
12, 18, 24, 30, 36, . . .
multiples of 9: 0, 9,
18, 27, 36, . . .
Zero is a multiple of every number, but it cannot be the LCM.
The LCM of 4, 6, and 9 is 36.
You can also use prime factorization to find the LCM.
4 = 2 ⋅ 2 6
= 2 ⋅ 3 9 = 3 ⋅ 3
The prime factors are 2 and 3. The greatest number of times 2
appears is twice (in 4). The greatest number of times 3 appears is twice (in
9). So, the LCM of 4, 6, and 9 is 2 ⋅
2 ⋅ 3 ⋅ 3 or 36. This is the same answer you
got by listing the multiples.
Find the LCM for each pair of expressions.
Teaching
Link
3. Mrs.
Reimer wants student groups of 4, 6, or 8. What is the minimum number of desks
needed?
Alternative Solutions:
Find
the LCM of 4, 6, and 8.
4 = 2 ⋅ 2
6 = 2 ⋅ 3
Mrs. Reimer
must have at least 24 desks in her classroom.
To add or subtract fractions with unlike denominators, first
rename the fractions so the denominators are alike. Any common denominator
could be used. However, the computation is usually easier if you use the least common denominator (LCD).
Recall that the least common denominator is the LCM of the denominators.
Example
Write each pair of rational expressions with the same LCD.
First
find the LCD.
LCD = 2 ⋅ 3 ⋅ m ⋅ m or 6m2
Then
write each fraction with the same LCD.
First
find the LCD.
LCD
= 4(x + 2)
Then
write each fraction with the same LCD.
Use the following steps to add or subtract rational
expressions with unlike denominators.
Example
Find each sum or difference. Write in simplest form.
Sumber
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