6.NOS.4 Lesson 6-12-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.12 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

Least Common Multiple · Multiple · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — What is the least common multiple (LCM)?
1The LCM is the FIRST number that shows up in both numbers' multiple lists — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
2Worked Example — Watch me
  1. I want the LCM of 4 and 6. I skip count the multiples of 4: 4, 8, 12, 16, 20, 24.
  2. Then I skip count the multiples of 6: 6, 12, 18, 24.
  3. I look for the first number in BOTH lists. 12 is in both lists, and it comes before 24.
  4. So the LCM of 4 and 6 is 12. I check: 12 ÷ 4 = 3 and 12 ÷ 6 = 2, so both go into 12 evenly.
3Second Model — Try it together — then prove it
  1. Let's find the LCM of 3 and 5. What are the multiples of 3? (3, 6, 9, 12, 15.)
  2. What are the multiples of 5? (5, 10, 15.) What is the first number in both lists? (15.)
  3. So the LCM of 3 and 5 is 15.
  4. Now prove it: say why that move had to work at all — not just that it did.
  5. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical 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.
5Watch 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

    What is the LCM of 6 and 8?

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

    What is the LCM of 4 and 10?

    1. A20
    2. B40
    3. C10
    4. D2
    ✏️ Workspace & Solution Steps
  3. 3 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. A9:00 AM (60 minutes later)
    2. B8:30 AM (30 minutes later)
    3. C8:40 AM (40 minutes later)
    4. D9:20 AM (80 minutes later)
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:What is the LCM of 6 and 8?
    2. 2A classmate at our table answered:48

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Spot Maya's Mistake — LCM of 6 and 9

    1. 1Problem:Find the LCM of 6 and 9.
    2. 2Multiples of 6:6, 12, 18, 24
    3. 3Multiples of 9:9, 18, 27
    4. 4Choose the answer:Maya saw that 9 is bigger than 6, so she wrote LCM = 9.

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Find Jaylen's Mistake

    1. 1Find LCM of 8 and 12:List multiples of 8 and 12
    2. 2Multiples of 8:8, 16, 24, 32, 40, 48
    3. 3Multiples of 12:12, 24, 36, 48
    4. 4Common multiples:24, 48
    5. 5Choose LCM:LCM = 48

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
📐 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