Questions: Greatest Common Factor and Least Common Multiple
4 questions to test your understanding
Score: 0 / 4
Question 1 Multiple Choice
What is the least common multiple of 4 and 6?
A2
B10
C12
D24
Multiples of 4 are 4, 8, 12, 16, ... and multiples of 6 are 6, 12, 18, ... The first shared multiple is 12. The product 24 is a common multiple but not the least one, because 4 and 6 share the factor 2.
Question 2 True / False
The LCM of two whole numbers is always equal to their product.
TTrue
FFalse
Answer: False
The product is a common multiple, but it is the least one only when the numbers share no factor other than 1. For 4 and 6 the product is 24 while the LCM is 12.
Question 3 Short Answer
Using prime factorizations 12 = 2² × 3 and 18 = 2 × 3², find the GCF and the LCM of 12 and 18.
Think about your answer, then reveal below.
Model answer: GCF = 2 × 3 = 6; LCM = 2² × 3² = 36
The GCF takes each shared prime to the smaller power (2¹ and 3¹). The LCM takes each prime that appears to the larger power (2² and 3²). As a check, GCF × LCM = 6 × 36 = 216 = 12 × 18.
Question 4 Multiple Choice
A teacher has 24 pencils and 36 erasers and wants identical kits with nothing left over. What is the greatest number of kits she can make?
A6
B12
C72
D60
Each kit count must divide both 24 and 36, so the largest number of kits is GCF(24, 36) = 12. Each kit then holds 2 pencils and 3 erasers. 72 is the LCM, which answers a different kind of question.