Question

vivian found the lcm of 3 and 6. her work is shown here.

multiples of 3: 3, 6, 9, 12, 15, ...
multiples of 6: 6, 12, 18, 24, 30, ...

the lcm is 12.

what was vivians error?

• the student needed to list more multiples for each number.
• the student listed factors of each number instead of multiples.
• the student should have multiplied 3 and 6 to find the lcm.
• the student selected a multiple that is not the least of the common multiples.

Explanation:

Analyze the student's work

The student listed:

• Multiples of 3: 3, 6, 9, 12, 15, ...
• Multiples of 6: 6, 12, 18, 24, 30, ...

The common multiples listed are 6 and 12.
The student selected 12 as the Least Common Multiple (LCM).

Identify the error

The smallest (least) of the common multiples is 6, not 12.
Therefore, the student selected a common multiple that is not the least.

Answer:

• The student needed to list more multiples for each number.
• The student listed factors of each number instead of multiples.
• The student should have multiplied 3 and 6 to find the LCM.
• The student selected a multiple that is not the least of the common multiples. (Correct answer)