# MATHCOUNTS TOOLBOX Lesson 1: Single Method for Finding Both the GCF and LCM

In this lesson of the MATHCOUNTS TOOLBOX, you will learn a single method that can help you find both

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## About MATHCOUNTS TOOLBOX Lesson 1: Single Method for Finding Both the GCF and LCM

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## Presentation Transcript

Slide1MATHCOUNTS TOOLBOX  Facts, Formulas and Tricks

Slide2Lesson 1:Single Method for finding both the GCF and LCM

Slide3 Put both numbers in a lattice.  On theleft, put ANY divisor of the two numbers and put the quotients below the original numbers.  Repeat until the quotients have no common factors except 1 (relatively prime).

Slide4 Put both numbers in a lattice.  On theleft, put ANY divisor of the two numbers and put the quotients below the original numbers.  Repeat until the quotients have no common factors except 1 (relatively prime).

Slide5 Put both numbers in a lattice.  On theleft, put ANY divisor of the two numbers and put the quotients below the original numbers.  Repeat until the quotients have no common factors except 1 (relatively prime).

Slide6 Put both numbers in a lattice.  On theleft, put ANY divisor of the two numbers and put the quotients below the original numbers.  Repeat until the quotients have no common factors except 1 (relatively prime).

Slide7 Draw a “boot” around the left-most column and the bottom row.  Multiply the vertical divisors to get the GCF. Multiply the “boot” numbers (vertical divisors and last-row quotients) to get the LCM.

Slide8 Draw a “boot” around the left-most column and the bottom row.  Multiply the  vertical divisors  to get the GCF. Multiply the “boot” numbers (vertical divisors and last-row quotients) to get the LCM. The GCF is 2 x 10 = 20

Slide9 Draw a “boot” around the left-most column and the bottom row.  Multiply the vertical divisors to get the GCF. Multiply the  “boot”  numbers (vertical divisors and last-row quotients) to get the LCM. The LCM is 2 x 10 x 2 x 7 = 280

Slide10 Fini!