GCF and LCM In Word Problems

Learning Objectives Distinguish between scenarios requiring GCF and those requiring LCM in word problems. Apply prime factorization to find the GCF of two or more numbers. Apply prime factorization to find the LCM of two or more numbers. Translate real-world word problems into mathematical problems involving GCF or LCM. Solve GCF and LCM word problems and interpret their answers in context. Verify their GCF and LCM calculations using the relationship between them for two numbers. Ever wondered how bakers figure out the largest equal batches of cookies and brownies they can make, or when two different bus routes will meet at the same stop again? 🚌🍪 These everyday puzzles are solved using GCF and LCM! In this lesson, you'll learn how to identify keywords and situations...

TermDefinitionExample FactorA factor of a number is a whole number that divides exactly into that number without leaving a remainder.The factors of 12 are 1, 2, 3, 4, 6, and 12. MultipleA multiple of a number is the product of that number and any whole number (excluding zero).The first five multiples of 7 are 7, 14, 21, 28, and 35. Greatest Common Factor (GCF)The GCF of two or more numbers is the largest factor that they share in common. It's used when you want to divide things into the largest possible equal groups.The GCF of 12 and 18 is 6, because 6 is the largest number that divides evenly into both 12 and 18. Least Common Multiple (LCM)The LCM of two or more numbers is the smallest non-zero multiple that they share in common. It's used when you want to find when events will...

Finding GCF using Prime Factorization To find the GCF of two or more numbers: 1. Find the prime factorization of each number. 2. Identify all common prime factors. 3. Multiply these common prime factors, using the lowest exponent for each common factor. This method is efficient for larger numbers and ensures you find the *greatest* common factor by only taking what all numbers share, and only the smallest power of those shared factors. Finding LCM using Prime Factorization To find the LCM of two or more numbers: 1. Find the prime factorization of each number. 2. List all unique prime factors from all numbers. 3. Multiply these unique prime factors, using the highest exponent for each factor. This method is efficient for larger numbers and ensures you find the *least* common...