Page 870 - Algebra 1

Least Common Multiple (LCM) and Least Common Denominator (LCD)
Skills Bank Lesson 10
The least common multiple, or LCM, is the smallest whole number, other than zero, that is a multiple of two or more given numbers.
Finding the LCM
a. Find the LCM of 6 and 10. SOLUTION
List the multiples of each number.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
Multiples of 10: 10, 20, 30, 40, 50, 60, ...
30 and 60 are common multiples. Find the common multiples that are in both lists. The LCM of 6 and 10 is 30. Find the least common multiple.
b. Find the LCM of 12 and 18. SOLUTION
2 12 18 Divide both numbers by the same prime factor.
Example
1
369
2 3 numbers without a remainder.
Keep dividing until there is no prime factor that divides into both
2·3·2·3or22 ·32 =36.TheLCMof 12and18is36.
The least common denominator, or LCD, is the least common multiple of two or more
denominators.
Finding the LCD and Writing Equivalent Fractions
Find the LCD of _3 and _5 . Use the LCD to write equivalent fractions. 8 12
SOLUTION The LCM of 8 and 12 is 24, so 24 is the LCD.
Example
2
3=3·3= 9 ___
_3 and _5 are equivalent to _9 and _10 .
Skills Bank Practice
8 8·3 24 5 = 5·2 =10
Writeanequivalentfractionusingadenominatorof24. Writeanequivalentfractionusingadenominatorof24.
___ 12 12 · 2 24
8 12
24 24
Find the LCM.
a. 9 and 15 b. 20 and 25
e. 25, 50, and 100 f. 8, 16, and 48
h. Use the LCD to write equivalent fractions for _1 and _7 . 2 15
c. 24 and 48
d. 14 and 21 g. 2, 3, and 20
Skills Bank 855
SKILLS BANK