6.NOS.4 Lesson 6-12-part2 Apply Day · Set B
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6.12 · Part II

Second Practice Form · Independent Application and Spiral Review

Least Common Multiple · Multiple

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■ ADVANCED CONCEPT ANCHOR: 6.12 · Part II
1Least Common Multiple (LCM)
2The Structural Procedure
  1. Skip count multiples of each number starting with the larger number
  2. Identify the first non-zero multiple that appears in both lists
  3. Prime factorization method: Product of highest powers of all prime factors
3Mathematical Word Bank
  • Least Common Multiple (Mínimo común múltiplo) — The least positive number that is a multiple of two or more numbers.
  • Multiple (Múltiplo) — What you get when you multiply a number by 1, 2, 3, and so on.
  • Common multiple (Múltiplo común) — A number that two or more numbers both go into.
  • Skip counting (Conteo salteado) — Counting by a number, like 2, 4, 6, to list its multiples.
  • Prime factorization (Factorización prima) — Writing a number as prime numbers multiplied together. It helps you find the LCM.
4Watch out
  • A common mistake in Least Common Multiple is multiplying the two numbers together instead of listing multiples to find the smallest shared one. For example, for 4 and 6, a student calculates 4 × 6 = 24 and calls that the LCM, but the actual least common multiple is 12 (multiples of 4: 4, 8, 12; multiples of 6: 6, 12 — 12 is the first number that appears in both lists). This shortcut only works when the two numbers share no common factors (like 4 and 9, where the LCM really is 36 = 4 × 9); for numbers like 4 and 6 that share a factor of 2, multiplying overshoots the true LCM. Always list multiples of both numbers and pick the first one that appears in both lists.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    (Lesson 6.13) Which of the following is a prime number?

    1. A17
    2. B15
    3. C21
    4. D9
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    (Lesson 6.13) What is the prime factorization of 30?

    1. A2 × 3 × 5
    2. B5 × 6
    3. C2 × 15
    4. D3 × 10
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    (Lesson 6.7) Using prime factors, 48 = 2 × 2 × 2 × 2 × 3 and 36 = 2 × 2 × 3 × 3. What is their GCF?

    1. A12, from the shared 2 × 2 × 3
    2. B144, from multiplying all the primes
    3. C6, from one 2 and one 3
    4. D2, the only prime they share
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    What is the LCM of 3 and 5?

    1. A15
    2. B3
    3. C5
    4. D30
    ✏️ Workspace & Solution Steps
  5. 5 MULTIPLE CHOICE

    What is the LCM of 6 and 8?

    1. A24
    2. B48
    3. C14
    4. D6
    ✏️ Workspace & Solution Steps
  6. 6 MULTIPLE CHOICE

    What is the LCM of 4 and 10?

    1. A20
    2. B40
    3. C10
    4. D2
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 7 OPEN RESPONSE

    You are making party favors. Glow sticks come in packs of 10 and bracelets come in packs of 4. What is the fewest of each you can buy so every favor has exactly one glow stick and one bracelet with none left over? Explain how the LCM solves this problem.

    ✏️ Mathematical Justification & Response
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It