Ms. Drake 7th grade Math

Number Theory

Lesson 6

Least Common Multiple

Number TheoryAddition Property of EqualityAlgebraic ExpressionBaseCoefficientComposite Number ConstantDivision Property of EqualityEquation

EvaluateExponentGreatest Common Factor (GFC)Inverse OperationsIsolate the VariableLeast Common Multiple (LCM)Like Terms

Number Theory

Number TheoryMultipleMultiplication Property of EqualityNumerical ExpressionOrder of OperationsPowerPrime FactorizationPrime NumberScientific NotationSolution

Number Theory

SolveStandard FormSubtraction Property Of EqualityTermVariableVerbal Expression

Use a list to find the Least Common Multiple (LCM)

4, 6, 12

4, 8, 12, 16, 24, 28, 32

6, 12, 18, 24, 30, 36

12, 24, 36, 48

Use Prime Factorization to find the LCM

78, 110Write the prime

factorization of each number.

Circle the common prime factors

78 = 2 3 13

110 = 2 5 11

List the prime factors of the numbers, using the circled

factorsonly once.2, 3, 5, 11, 13

9, 27, 45

9 = 3 327 = 3 3 345 = 3 3 5

3 3 3 5 = 135

2 ∙ 3 ∙ 5 ∙ 11 ∙ 13

Multiply the numbers in the list.

2, 3, 5, 11, 13

A cat runs a mile every 2 minutes. A squirrel runs a

mile every 5 minutes. A cat and a squirrel start

together running around a 1-mile track. How long will it be before they meet at

the starting point.

The sanitation department picks up recyclable plastics

every 3 days. The paper recycling picks up paper

every four days. They both picked up on May 4. When

will they next pick up on the same day?

Juan and his mom plant a vegetable garden. Juan planted a row every 30 minutes and his mom

planted a row every 20 minutes. If they started

together, how long before it will be before they both finish a row together?

Until next time, try the following word problem…

Jasmine is helping her father plant trees. She plants a

tree every 25 minutes, and her father plants a tree

every 15 minutes. If they start together,

how long before they would finish planting a tree at the

same time?