6.NCC.12: Least Common Multiple
Finding the LCM of Two Numbers
What is the least common multiple of 6 and 8?
A. 24
B. 48
C. 14
D. 18
Answer: A. 24
Explanation:
Multiples of 6: 6, 12, 18, 24, 30...
Multiples of 8: 8, 16, 24, 32...
✅ The smallest number in common is 24
Comparing Means (6.SP.8a)
Two basketball teams recorded the number of points scored in 5 games:
Team A: 50, 55, 60, 65, 70
Team B: 60, 60, 60, 60, 60
Which team has a higher mean score?
A. Team A
B. Team B
C. Both have the same mean
D. Not enough information
Answer: C. Both have the same mean
Explanation:
Team A's mean = (50 + 55 + 60 + 65 + 70) ÷ 5 = 60
Team B's mean = all values are 60 → mean = 60
Area of a Rectangle
A rectangle has a length of 12 cm and a width of 5 cm.
What is the area of the rectangle?
A. 17 cm²
B. 60 cm²
C. 30 cm²
D. 24 cm²
Answer: B. 60 cm²
Explanation: Area of a rectangle = length × width = 12 × 5 = 60 cm²
Identifying a Statistical Question (6.SP.1)
Which of the following is a statistical question?
A. What is your favorite color?
B. How old is your teacher?
C. How many pets do students in our class have?
D. What is 25 + 16?
Answer: C. How many pets do students in our class have?
Explanation: A statistical question expects variability in the data and requires data collection from a group. Options A and B ask about individuals.
Option D is a math problem, not a question for data.
Option C involves a group and can have many different answers.
Understanding Data Distribution (6.SP.5a)
Which of the following describes a data set with a symmetric distribution?
A. Most values are on the low end, with a few very high values.
B. The data values are evenly spread on both sides of the center.
C. All values are the same.
D. Most values are clustered at the high end.
Answer: B. The data values are evenly spread on both sides of the center.
Explanation: A symmetric distribution means the data is balanced around the center—like a mirror image.
Real-World LCM Problem
A gym class does jumping jacks every 4 days and push-ups every 6 days. If they did both today, in how many days will they do both again on the same day?
A. 10
B. 12
C. 24
D. 18
Answer: B. 12
Explanation:
LCM of 4 and 6 is 12, so both exercises align every 12 days
Comparing Variability (6.SP.8b)
Using the same data above, which team shows less variability in their performance?
A. Team A
B. Team B
C. Both have equal variability
D. Can't tell without median
Answer: B. Team B
Explanation: Team B's scores are all the same (60), so there is no variability. Team A’s scores vary from 50 to 70.
Area of a Triangle
A triangle has a base of 10 inches and a height of 6 inches.
What is the area of the triangle?
A. 30 in²
B. 60 in²
C. 16 in²
D. 36 in²
Answer: A. 30 in²
Explanation: Area of a triangle = (1/2) × base × height
= (1/2) × 10 × 6 = 30 in²
Mean (6.SP.2)
The test scores of five students are:
78, 85, 90, 87, 80
What is the mean score?
A. 84
B. 86
C. 85
D. 83
Answer: A. 84
Explanation:
Add all scores: 78 + 85 + 90 + 87 + 80 = 420
Divide by number of scores: 420 ÷ 5 = 84
Measures of Center (6.SP.5c)
Which measure of center would be most affected by an outlier?
A. Mean
B. Median
C. Mode
D. Range
Answer: A. Mean
Explanation: The mean is sensitive to extreme values (outliers), which can pull it higher or lower.
Using Prime Factorization to Find LCM
Find the LCM of 9 and 15 using prime factorization.
A. 45
B. 90
C. 30
D. 135
Answer: A. 45
Explanation:
9 = 3²
15 = 3 × 5
LCM = 3² × 5 = 45
Making Inferences (6.SP.9)
Class 1 and Class 2 both took the same science test.
Class 1 scores: 78, 80, 82, 84, 86
Class 2 scores: 70, 75, 80, 85, 90
Which class has a more consistent performance?
A. Class 1
B. Class 2
C. Both are equal
D. Can't tell
Answer: A. Class 1
Explanation:
Class 1 scores are tightly grouped with a smaller range (86–78 = 8).
Class 2 scores have a wider range (90–70 = 20), showing more variability.
Surface Area of a Cube
Each edge of a cube is 4 cm long.
What is the surface area of the cube?
A. 96 cm²
B. 64 cm²
C. 48 cm²
D. 36 cm²
Answer: A. 96 cm²
Explanation: A cube has 6 faces. Area of one face = 4 × 4 = 16 cm²
Surface area = 6 × 16 = 96 cm²
What is the median of this data set?
12, 17, 15, 10, 20
A. 15
B. 17
C. 14
D. 12
Answer: A. 15
Explanation:
Order the numbers: 10, 12, 15, 17, 20
The middle number is 15 → that's the median
Analyzing Spread (6.SP.5b)
What does the range of a data set tell you?
A. The most common value
B. The average of all the values
C. How many values are in the data set
D. The difference between the highest and lowest values
Answer: D. The difference between the highest and lowest values
Explanation: The range shows how spread out the data is.
Comparing LCMs
Which pair of numbers has an LCM of 36?
A. 6 and 9
B. 4 and 9
C. 3 and 6
D. 12 and 18
Answer: B. 4 and 9
Explanation:
LCM of 4 and 9 = 36
(They are relatively prime, so LCM = 4 × 9 = 36)
Interpreting Measures of Center (6.SP.8)
Two groups of students recorded the number of books read over the summer:
Group A: Mean = 8 books, Median = 8 books
Group B: Mean = 10 books, Median = 7 books
Which group most likely has an outlier?
A. Group A
B. Group B
C. Both
D. Neither
Answer: B. Group B
Explanation: In Group B, the mean is higher than the median, suggesting a few larger values (outliers) are pulling the mean up.
Volume of a Rectangular Prism
A rectangular prism has a length of 8 cm, a width of 3 cm, and a height of 2 cm.
What is the volume of the prism?
A. 48 cm³
B. 24 cm³
C. 16 cm³
D. 96 cm³
Answer: A. 48 cm³
Explanation: Volume = length × width × height
= 8 × 3 × 2 = 48 cm³
Find the mode of the following data set:
5, 8, 5, 10, 6, 8, 5
A. 5
B. 8
C. 10
D. 6
Answer: A. 5
Explanation:
5 appears three times, more than any other number. The mode is the number that appears most often.
Describing a Data Set (6.SP.5d)
A class collected data on how many minutes they read per night:
15, 30, 25, 20, 30, 30, 40, 35, 30, 20
Which of the following best describes the distribution?
A. The data is centered around 30 with low variability.
B. The data has no mode and is widely spread.
C. The data is skewed to the left.
D. The data is very inconsistent.
Answer: A. The data is centered around 30 with low variability.
Explanation: The mode is 30, which appears most often. The values are fairly close to each other (range is 40–15 = 25), so spread is low.
LCM Application with Multiple Items
Lisa practices piano every 5 days and guitar every 7 days. If she starts both on Monday, how many days until she practices both again on the same day?
A. 35
B. 12
C. 30
D. 40
Answer: A. 35
Explanation:
LCM of 5 and 7 = 35
She will practice both again on the 35th day
Choosing the Best Measure (6.SP.9)
You want to compare two data sets where one contains extreme values.
Which measure of center is most reliable?
A. Mean
B. Mode
C. Median
D. Range
Answer: C. Median
Explanation: The median is not affected by outliers, making it a better choice when data includes extreme values.
Maria wants to paint the outside of a box (10 in long, 5 in wide, and 4 in high).
How much surface area will she paint?
A. 180 in²
B. 240 in²
C. 220 in²
D. 200 in²
Answer: C. 220 in²
Surface area of a rectangular prism = 2(lw + lh + wh)
Now calculate:
= 2(10×5 + 10×4 + 5×4) = 2(50 + 40 + 20) = 2(110) = 220 in²
Statistical Thinking (6.SP.1 & 6.SP.2)
A class collected data on how many books each student read last month:
3, 5, 2, 6, 5, 4, 3, 7, 5, 3
What is the mean number of books read?
A. 4.3
B. 4.5
C. 5
D. 3.5
Answer: A. 4.3
Explanation:
Add: 3+5+2+6+5+4+3+7+5+3 = 43
Divide: 43 ÷ 10 = 4.3
✅ Corrected Answer: A. 4.3
Interpreting Data (6.SP.5c & 6.SP.5d)
Two classes recorded how many pencils each student had:
Class A: 2, 3, 3, 4, 4, 4, 5, 5
Class B: 1, 2, 2, 3, 10, 12, 15
Which class has a greater spread in the data?
A. Class A
B. Class B
C. Both have the same spread
D. Not enough data
Answer: B. Class B
Explanation: Class A’s values range from 2 to 5 (range = 3).
Class B’s values range from 1 to 15 (range = 14). So, Class B has a greater spread.