LCM, LCD
CONCEPTS
Definitions
• LCM (least common multiple): smallest multiple amongst several numbers or variables
EXAMPLE
Numbers: 10, 20
Factors for each number: 10 = 5 * 2, 20 = 5 * 2 * 2
Minimum factors divisible for all numbers = 5, 2, 2
Multiply factors together to get the LCM = 5 * 2 * 2 = 20
• LCD (least common denominator): smallest common denominator for several fractions. It is used to add/subtract fractions
EXAMPLE
• Numbers = 1/5 & 1/2 => LCD = 10
PRACTICE PROBLEMS
Question 1 What is the LCM of 30, 20, & 70?
-- Answer -- 420
30 = 3 * 2 * 5 20 = 2 * 5 * 2 70 = 7 * 5 * 2
3 * 2 * 2 * 5 * 7 = 420
Question 2 What is the LCD of 4/21, 1/12, & 3/8?
-- Answer -- 1/168
21 = 7 * 3, 12 = 2 * 2 * 3, 8 = 2 * 2 * 2
7 * 3 * 2 * 2 * 2 = 168
ACT PRACTICE PROBLEMS