Greatest Common Factor and Least Common Multiple: Sample FAST Questions
Students find the greatest common factor (GCF) and least common multiple (LCM) of two whole numbers, both as straight computation and within real-world contexts. Typical applications include splitting items into equal groups (GCF) or figuring out when two repeating events line up again (LCM).
How the FAST tests this benchmark
FAST items include equation editor questions asking for the GCF or LCM of two numbers and multiple choice word problems where students must recognize whether a situation calls for GCF or LCM.
Skills students need
Find the greatest common factor of two whole numbers
Find the least common multiple of two whole numbers
Solve real-world problems using GCF and LCM
Try 4 real MA.6.NSO.3.1 questions
These come straight from Algebro's question bank. Pick an answer to check it instantly.
Question 1EasyEquation Editor
What is the greatest common factor (GCF) of 18 and 30?
Enter the number only. Do not include units like $, %, or ft²
Correct answer: 6
This explanation shows one way to solve the problem.
Factors of 18: 1,2,3,6,9,18
Factors of 30: 1,2,3,5,6,10,15,30
Find the GCF: Common factors: 1,2,3,6 → GCF =6
Final Answer
6
Question 2MediumMultiple Choice
A florist has 16 roses and 40 tulips. She wants to make identical bunches with the same number of each flower in every bunch. What is the greatest number of bunches she can make?
Correct answer: C. 8
This explanation shows one way to solve the problem.
Recognize as GCF: Identical groups, no leftovers → need GCF(16, 40)
Find the prime factorization: 16=24,40=23×5
Take the lowest power of each common prime: Common prime: 2. Lowest power: 23
Multiply: 23=8
Final Answer
8
Question 3MediumMultiple Choice
What is the least common multiple (LCM) of 8,10, and 12?
Correct answer: C. 120
This explanation shows one way to solve the problem.
Find the prime factorization: 8=23,10=2×5,12=22×3
Take the highest power of each prime: 23,31,51
Multiply: 23×3×5=8×3×5=120
Final Answer
120
Question 4HardMultiple Choice
Two gears start aligned. One completes a rotation every 9 seconds and the other every 15 seconds. After how many seconds will the gears be aligned again?
Correct answer: C. 45 seconds
This explanation shows one way to solve the problem.
Recognize as LCM: First time both coincide → LCM(9, 15)
Multiples of 9: 9,18,27,36,45,54,…
Multiples of 15: 15,30,45,60,…
Find the LCM: Smallest shared multiple → LCM =45
Final Answer
45 seconds
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