Lesson Plan

Find the greatest common factor (GCF) of two whole numbers <= 100 by listing factors of each and identifying the largest common factor.

Find the GCF using prime factorization -- decomposing each number into primes and taking the product of common primes at lowest power.

Find the least common multiple (LCM) of two whole numbers <= 12 by listing multiples of each and identifying the smallest common multiple.

Find the LCM using prime factorization -- taking the product of all primes appearing in either factorization at their highest power.

Use the distributive property to express a sum of two whole numbers (1-100) with a common factor as the GCF times a sum of two coprime whole numbers (e.g., 36 + 8 = 4(9 + 2)).

Recognize from a real-world context whether GCF or LCM is the appropriate tool: GCF for partition problems ("largest equal group"), LCM for alignment problems ("when do they next coincide").

6.NS.B.4

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). -- Standard 6.NS.B.4