GCF and LCM: word problems

Learning Objectives Identify keywords in word problems that indicate the need for GCF or LCM. Determine whether a word problem requires finding the GCF or the LCM of given numbers. Apply prime factorization or listing methods to find the GCF of two or more numbers. Apply prime factorization or listing methods to find the LCM of two or more numbers. Solve real-world word problems involving GCF and LCM. Explain the reasoning behind choosing GCF or LCM to solve a specific problem. Ever wonder how many identical gift baskets you can make from a pile of items, or when two buses will arrive at the station at the same time again? 🤔 Math can help us figure it out! In this lesson, you'll learn how to tackle word problems by deciding whether to use the Greatest Common Factor (G...

TermDefinitionExample FactorA number that divides another number exactly, leaving no remainder.The factors of 12 are 1, 2, 3, 4, 6, 12. MultipleThe product of a number and any whole number (except zero).The multiples of 3 are 3, 6, 9, 12, 15, ... Greatest Common Factor (GCF)The largest factor that two or more numbers share.The GCF of 12 and 18 is 6. Least Common Multiple (LCM)The smallest positive multiple that two or more numbers share.The LCM of 4 and 6 is 12. Prime FactorizationBreaking down a number into a product of its prime factors.The prime factorization of 12 is $2 \times 2 \times 3$ or $2^2 \times 3$. GCF KeywordsWords or phrases in a word problem that suggest finding the GCF.Keywords like 'divide', 'share', 'split', 'group', 'cut&#03...

Finding GCF using Prime Factorization To find the GCF of two or more numbers, first find the prime factorization of each number. Then, multiply the common prime factors, using the lowest power (exponent) for each common factor. Use this rule when you need to divide items into the largest possible equal groups, or find the maximum size of something that fits perfectly into different dimensions. Finding LCM using Prime Factorization To find the LCM of two or more numbers, first find the prime factorization of each number. Then, multiply all prime factors from all numbers, using the highest power (exponent) for each factor. Use this rule when you need to find when events will happen again at the same time, or find the smallest quantity that can be divided evenly by different nu...