What Are GCF and LCM Word Problems?

Greatest common factor and least common multiple word problems are math problems that pose a GCF or LCM question in a real-life situation. A GCF is the largest number that divides into two or more numbers without leaving a remainder, while a LCM is the smallest positive number that is a multiple of two or more numbers.

An example of a GCF word problem is, "Joanne is campaigning for class president and wants to distribute 20 flyers and 36 buttons. She wants each classroom to receive an identical set of campaign materials without having any left over. What is the greatest number of classrooms Joanne can deliver materials to?"

To find the GCF of two numbers such as 20 and 36, the factors of both numbers need to be compared to each other. The factors of 20, the numbers that 20 can be divided by without leaving a remainder, are 1, 2, 4, 5, 10 and 20. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. The factors that both numbers have in common are 1, 2 and 4. Of these, the highest is 4. Therefore, 4 is the GCF of 20 and 36. The answer to the GCF word problem is "four classrooms."

An example of a LCM word problem is, "Matthew goes hiking every 12 days and swimming every 16 days. He did both kinds of exercise today. In how many days will he go both hiking and swimming again?"

To find the LCM of two numbers such as 12 and 16, the multiples of the two numbers need to be compared to each other. The first few multiples of 12 are 12, 24, 36, 48, 60, 72, 84 and 96. The first few multiples of 16 are 16, 32, 48, 64, 80 and 96. From this small sample of multiples, 12 and 16 have 48 and 96 in common. Of these, 48 is the lowest number, so 48 is the LCM of 12 and 16. The answer to the LCM word problem is, "in 48 days."