GCF and LCM: word problems

Learning Objectives Identify keywords and phrases that indicate a GCF word problem. Identify keywords and phrases that indicate an LCM word problem. Apply prime factorization to find the GCF of two or more numbers. Apply prime factorization to find the LCM of two or more numbers. Solve real-world problems requiring the calculation of GCF. Solve real-world problems requiring the calculation of LCM. Ever wondered how many identical gift bags you can make from a pile of different items, or when two buses will arrive at the same stop again? 🤔 Math helps us solve these real-life puzzles! In this lesson, you'll learn to distinguish between Greatest Common Factor (GCF) and Least Common Multiple (LCM) problems, especially when they're hidden in word problems. Understandi...

TermDefinitionExample Greatest Common Factor (GCF)The largest number that divides exactly into two or more numbers without leaving a remainder.The GCF of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 evenly. Least Common Multiple (LCM)The smallest positive number that is a multiple of two or more numbers.The LCM of 4 and 6 is 12, because 12 is the smallest number that is a multiple of both 4 (4, 8, 12...) and 6 (6, 12...). FactorA number that divides another number exactly, without leaving a remainder.The factors of 12 are 1, 2, 3, 4, 6, and 12. MultipleThe result of multiplying a number by an integer. Multiples are like counting by that number.The first few multiples of 3 are 3, 6, 9, 12, 15, and so on. Prime FactorizationExpressing a composite number as a...

Rule for Finding GCF using Prime Factorization 1. Find the prime factorization of each number. 2. Identify all *common* prime factors. 3. For each common prime factor, take the one with the *lowest* exponent. 4. Multiply these selected prime factors together. Use this rule when a word problem asks you to divide items into the largest possible equal groups, find the maximum number of identical sets, or determine the largest common divisor. Rule for Finding LCM using Prime Factorization 1. Find the prime factorization of each number. 2. Identify *all unique* prime factors (common and non-common). 3. For each unique prime factor, take the one with the *highest* exponent. 4. Multiply these selected prime factors together. Use this rule when a word problem asks you to find...