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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

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