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**MATHCOUNTS TOOLBOX Facts, Formulas and Tricks**

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**Lesson 1: Single Method for finding both the GCF and LCM**

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**Put both numbers in a lattice**

Put both numbers in a lattice. On the left, 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).

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**Put both numbers in a lattice**

Put both numbers in a lattice. On the left, 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).

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**Put both numbers in a lattice**

Put both numbers in a lattice. On the left, 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).

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**Put both numbers in a lattice**

Put both numbers in a lattice. On the left, 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).

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**Draw a “boot” around the left-most column and the bottom row**

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.

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**Draw a “boot” around the left-most column and the bottom row**

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

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**Draw a “boot” around the left-most column and the bottom row**

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

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