lcm of 6 and 28
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 6 and 28. To find the LCM, we will identify the multiples of both numbers and determine the smallest multiple that they have in common.
Answer
$84$
Answer for screen readers
The least common multiple (LCM) of 6 and 28 is $84$.
Steps to Solve
- Identify the multiples of each number
Start by listing a few multiples of both numbers.
For 6, the first few multiples are:
- $6, 12, 18, 24, 30, 36, 42, 48, 54, 60, \ldots$
For 28, the first few multiples are:
- $28, 56, 84, 112, 140, \ldots$
- Find the common multiples
Next, we look for any common multiples in the lists we have created.
From the multiples listed:
- The multiples of 6: $6, 12, 18, 24, 30, 36, 42, 48, 54, 60, \ldots$
- The multiples of 28: $28, 56, 84, 112, 140, \ldots$
The first common multiple we notice is $84$.
- Verify that it is indeed the least common multiple (LCM)
To verify, both numbers should divide $84$ with no remainder:
Calculating for 6: $$ 84 \div 6 = 14 $$ (This is an integer, so 6 divides 84)
Calculating for 28: $$ 84 \div 28 = 3 $$ (This is also an integer, so 28 divides 84)
Since both divisions result in integers and $84$ is the smallest common multiple we found, we conclude that this is the LCM.
The least common multiple (LCM) of 6 and 28 is $84$.
More Information
The least common multiple is useful in problems involving fractions, adding and subtracting fractions, and other mathematical operations where common denominators are necessary. In this case, $84$ is also the smallest positive integer that is a multiple of both $6$ and $28$.
Tips
One common mistake is overlooking smaller common multiples or mistakenly assuming that larger multiples are the smallest. To avoid this, always verify by checking divisibility of the found LCM by both original numbers.
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