Grade 6 Least Common Multiple Practice Test

Correct answer: A

The correct answer is The smallest positive multiple shared by two or more numbers..

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: The LCM is the first positive value that appears in the multiple lists of all the numbers.
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 24 is a multiple of both numbers..

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: A common multiple is divisible by every number in the group, so 24 is divisible by both.
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 The greatest exponent includes enough factors to make the result divisible by every number..

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: The LCM must contain every prime factor required by each number, using the largest power that appears.
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 The larger number.

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: The larger number is already a multiple of both, and no positive common multiple can be smaller than it in this situation.
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 $22$.

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: Since 22 is a multiple of 11, $LCM(11,22) = 22$.
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 Choosing the GCF instead of the LCM..

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: Repeating events align at a common multiple, and the first alignment uses the LCM.
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: The multiples are 6, 12, 18, 24 and 8, 16, 24, so the first shared value is 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 $x = 12$.

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: $12 \div 4 = 3$ and $12 \div 6 = 2$, so 12 is the least positive common multiple.
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 Check that it is divisible by every number and that no smaller positive common multiple exists..

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: Both the common-multiple condition and the least-positive condition are required.
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 The LCM is the smallest positive multiple shared by numbers and helps solve repeating schedules, synchronization, and common-denominator problems..

1. List the multiples: Write multiples of each number or use prime factorization.
2. Find the first shared multiple: A complete summary connects multiples, prime factorization, schedules, synchronization, and fraction applications.
3. Check the result: Verify that the answer is divisible by every number and that no smaller positive common multiple works.