Grade 6 Least Common Multiple Practice Test

Correct answer: A

The correct answer is $36$.

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: $12 = 2^2 \times 3$ and $18 = 2 \times 3^2$. Use the greatest powers: $2^2 \times 3^2 = 36$.
3. Check the result: Verify that the answer is divisible by every number and that no smaller positive common multiple works.

Correct answer: B

The correct answer is $60$.

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: $20 = 2^2 \times 5$ and $30 = 2 \times 3 \times 5$. The LCM is $2^2 \times 3 \times 5 = 60$.
3. Check the result: Verify that the answer is divisible by every number and that no smaller positive common multiple works.

Correct answer: C

The correct answer is $24$.

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: $8 = 2^3$ and $12 = 2^2 \times 3$. Use $2^3 \times 3 = 24$.
3. Check the result: Verify that the answer is divisible by every number and that no smaller positive common multiple works.

Correct answer: D

The correct answer is $42$.

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: $14 = 2 \times 7$ and $21 = 3 \times 7$, so $2 \times 3 \times 7 = 42$.
3. Check the result: Verify that the answer is divisible by every number and that no smaller positive common multiple works.

Correct answer: A

The correct answer is $60$.

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: $15 = 3 \times 5$ and $20 = 2^2 \times 5$. The LCM is $2^2 \times 3 \times 5 = 60$.
3. Check the result: Verify that the answer is divisible by every number and that no smaller positive common multiple works.

Correct answer: B

The correct answer is $36$.

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: $9 = 3^2$ and $12 = 2^2 \times 3$. Use $2^2 \times 3^2 = 36$.
3. Check the result: Verify that the answer is divisible by every number and that no smaller positive common multiple works.

Correct answer: C

The correct answer is $48$.

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: $16 = 2^4$ and $24 = 2^3 \times 3$. Use $2^4 \times 3 = 48$.
3. Check the result: Verify that the answer is divisible by every number and that no smaller positive common multiple works.

Correct answer: D

The correct answer is $54$.

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: $18 = 2 \times 3^2$ and $27 = 3^3$. Use $2 \times 3^3 = 54$.
3. Check the result: Verify that the answer is divisible by every number and that no smaller positive common multiple works.

Correct answer: A

The correct answer is $150$.

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: $25 = 5^2$ and $30 = 2 \times 3 \times 5$. Use $2 \times 3 \times 5^2 = 150$.
3. Check the result: Verify that the answer is divisible by every number and that no smaller positive common multiple works.

Correct answer: B

The correct answer is $84$.

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: $28 = 2^2 \times 7$ and $42 = 2 \times 3 \times 7$. Use $2^2 \times 3 \times 7 = 84$.
3. Check the result: Verify that the answer is divisible by every number and that no smaller positive common multiple works.