a) list the first 10 positive multiples of 9, starting with $1 \cdot 9 = 9$.
b) list the first 10 positive multiples of 3, starting with $1 \cdot 3 = 3$.
c) use parts a) and b) to determine the least natural number that is a multiple of both 9 and 3.

a) the first 10 positive multiples of 9 are
(use a comma to separate answers as needed.)

Question

a) list the first 10 positive multiples of 9, starting with $1 \cdot 9 = 9$.
b) list the first 10 positive multiples of 3, starting with $1 \cdot 3 = 3$.
c) use parts a) and b) to determine the least natural number that is a multiple of both 9 and 3.

a) the first 10 positive multiples of 9 are
(use a comma to separate answers as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Least Common Multiple", "Multiples of Numbers" ], "current_concepts": [ "Multiples of Numbers", "Least Common Multiple" ] } ## Find the first 10 positive multiples of 9 $$ \begin{aligned} &1 \cdot 9 = 9, \quad 2 \cdot 9 = 18, \quad 3 \cdot 9 = 27, \quad 4 \cdot 9 = 36, \quad 5 \cdot 9 = 45, \ &6 \cdot 9 = 54, \quad 7 \cdot 9 = 63, \quad 8 \cdot 9 = 72, \quad 9 \cdot 9 = 81, \quad 10 \cdot 9 = 90 \end{aligned} $$ ## Find the first 10 positive multiples of 3 $$ \begin{aligned} &1 \cdot 3 = 3, \quad 2 \cdot 3 = 6, \quad 3 \cdot 3 = 9, \quad 4 \cdot 3 = 12, \quad 5 \cdot 3 = 15, \ &6 \cdot 3 = 18, \quad 7 \cdot 3 = 21, \quad 8 \cdot 3 = 24, \quad 9 \cdot 3 = 27, \quad 10 \cdot 3 = 30 \end{aligned} $$ ## Determine the least common multiple $$ \begin{aligned} &M_9 = \{9, 18, 27, 36, 45, 54, 63, 72, 81, 90\} \ &M_3 = \{3, 6, 9, 12, 15, 18, 21, 24, 27, 30\} \ &M_9 \cap M_3 = \{9, 18, 27, \dots\} \ &\min(M_9 \cap M_3) = 9 \end{aligned} $$ ## Question a The first 10 positive multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90. ## Question b The first 10 positive multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. ## Question c The least natural number that is a multiple of both 9 and 3 is 9. { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Least Common Multiple" ] }

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Question

Explanation:

Find the first 10 positive multiples of 9

Find the first 10 positive multiples of 3

Determine the least common multiple

Answer:

Question a

Question b

Question c