A focused Grade 6 learning session for Greatest Common Factor and Least Common Multiple using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving greatest common factor and least common multiple.
Greatest Common Factor and Least Common Multiple means choosing a model, naming what each number means, and explaining the strategy.
Question: Find the LCM of \(12\) and \(15\) using the table below.
| Multiples of 12 | 12 | 24 | 36 | 48 | 60 | 72 |
|---|---|---|---|---|---|---|
| Multiples of 15 | 15 | 30 | 45 | 60 | 75 | 90 |
Why it works: Looking at the table, the first number that appears in both rows is \(60\). This is the least common multiple.
Answer: \(60\)
Question: What is the greatest common factor (GCF) of \(24\) and \(36\)?
Answer: \(12\)
Question: Which list contains all factors of \(20\)?
Answer: \(1, 2, 4, 5, 10, 20\)
Question: A teacher wants to divide \(24\) students into equal groups with no students left over. Which group size is NOT possible?
Why it works: The factors of \(24\) are \(1, 2, 3, 4, 6, 8, 12, 24\). Since \(5\) is not a factor of \(24\), we cannot divide equally into groups of \(5\).
Answer: \(5\) students per group
Greatest Common Factor and Least Common Multiple becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
What is the greatest common factor (GCF) of \(24\) and \(36\)?
Answer C: \(12\)
List what both numbers share evenly: candidates include \(12\), since \(24 = 12 \times 2\) and \(36 = 12 \times 3\). Nothing larger divides both cleanly, so the GCF settles at \(12\).
Which list contains all factors of \(20\)?
Answer A: \(1, 2, 4, 5, 10, 20\)
When we divide \(20\) by each number: \(20 \div 1 = 20\), \(20 \div 2 = 10\), \(20 \div 4 = 5\), \(20 \div 5 = 4\), \(20 \div 10 = 2\), \(20 \div 20 = 1\). All these are factors.
What is the least common multiple (LCM) of \(6\) and \(8\)?
Answer A: \(24\)
Multiples of \(6\): \(6, 12, 18, 24, 30, \ldots\). Multiples of \(8\): \(8, 16, 24, 32, \ldots\). The least common multiple is \(24\).
Which pair of numbers has a GCF of \(5\)?
Answer A: \(15\) and \(25\)
Factors of \(15\): \(1, 3, 5, 15\). Factors of \(25\): \(1, 5, 25\). Common factors: \(1, 5\). GCF is \(5\). For option B, GCF is \(10\); for C, GCF is \(4\); for D, GCF is \(7\).
What is the GCF of \(16\) and \(40\)?
Answer D: \(8\)
Factors of \(16\): \(1, 2, 4, 8, 16\). Factors of \(40\): \(1, 2, 4, 5, 8, 10, 20, 40\). The greatest common factor is \(8\).
Which is a multiple of both \(4\) and \(6\)?
Answer B: \(12\)
\(12 = 4 \times 3\) and \(12 = 6 \times 2\), so \(12\) is divisible by both \(4\) and \(6\). Option A is a multiple of \(4\) but not \(6\); C is a multiple of \(6\) but not \(4\); D is neither.
What is the GCF of \(18\), \(27\), and \(45\)?
Answer B: \(9\)
Factors of \(18\): \(1, 2, 3, 6, 9, 18\). Factors of \(27\): \(1, 3, 9, 27\). Factors of \(45\): \(1, 3, 5, 9, 15, 45\). Common to all three: \(1, 3, 9\). GCF is \(9\).
Find the LCM of \(5\) and \(9\).
Answer A: \(45\)
Multiples of \(5\): \(5, 10, 15, 20, 25, 30, 35, 40, 45, \ldots\). Multiples of \(9\): \(9, 18, 27, 36, 45, \ldots\). The least common multiple is \(45\) because \(5\) and \(9\) share no common factors.
What is the prime factorization of \(30\)?
Answer A: \(2 \times 3 \times 5\)
\(30 = 2 \times 15 = 2 \times 3 \times 5\). The prime factors are \(2, 3, 5\). Option B uses \(15\), which is composite; C uses \(10\), which is composite; D gives prime factorization of \(12\).
What is the GCF of \(15\) and \(35\)?
Answer B: \(5\)
Factors of \(15\): \(1, 3, 5, 15\). Factors of \(35\): \(1, 5, 7, 35\). Common factors: \(1, 5\). GCF is \(5\). Distractors: \(3\) divides \(15\) only; \(7\) divides \(35\) only; \(15\) is the largest number but not the GCF.
Find the LCM of \(12\) and \(15\) using the table below.
Answer D: \(60\)
Looking at the table, the first number that appears in both rows is \(60\). This is the least common multiple.
