6.NOS.4 Lesson 6-12-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.12 · Part II

Supported Application · Guided Entry to Today's Problem

Least Common Multiple · Multiple

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 6.12 · Part II
1Least Common Multiple (LCM)
2Strategy Model — step by step
  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.
  1. 1 MULTIPLE CHOICE

    What is the LCM of 2 and 7?

    1. A2
    2. B7
    3. C9
    4. D14
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    (Lesson 6.7) Which list shows all the factors of 12?

    1. A1, 2, 3, 4, 6, 12
    2. B1, 12
    3. C2, 3, 4, 6
    4. D12, 24, 36, 48
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    (Lesson 6.7) Which list shows the first four multiples of 8?

    1. A1, 2, 4, 8
    2. B2, 4, 6, 8
    3. C8, 16, 24, 32
    4. D8, 9, 10, 11
    ✏️ Workspace & Solution Steps
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

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

C Claim
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It
6.NOS.4 Lesson 6-12-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.12 · Part II

On-Level Application · Standard Rigor

Least Common Multiple · Multiple

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ 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.
  1. 1 MULTIPLE CHOICE

    Two buses leave the station at 8:00 AM. Bus A returns every 15 minutes and Bus B returns every 20 minutes. When is the next time both buses are at the station together?

    1. A8:30 AM (30 minutes later)
    2. B8:40 AM (40 minutes later)
    3. C9:00 AM (60 minutes later)
    4. D9:20 AM (80 minutes later)
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    One machine runs every 4 min, another every 6 min. They just ran together. In how many minutes do they run together again?

    1. A6
    2. B10
    3. C12
    4. D24
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    One ship docks every 8 min, another every 12 min. They just docked together. In how many minutes do they dock together again?

    1. A16
    2. B20
    3. C24
    4. D48
    ✏️ Workspace & Solution Steps
📐 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
6.NOS.4 Lesson 6-12-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.12 · Part II

Extension & Non-Routine Application

Least Common Multiple · Multiple

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ 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.
  1. 1 MULTIPLE CHOICE

    What is the least common multiple of 6 and 8?

    1. A2
    2. B14
    3. C24
    4. D48
    ✏️ Workspace & Solution Steps
📐 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