What is the LCM of 21 and 28?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 21 and 28. To solve this, we will identify the multiples of both numbers and find the smallest one that they both share.
Answer
$84$
Answer for screen readers
The least common multiple of 21 and 28 is $84$.
Steps to Solve
- List the multiples of each number
First, we will list out some multiples of 21 and 28 to find the smallest common one.
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The multiples of 21 are: $$ 21, 42, 63, 84, 105, 126, \ldots $$
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The multiples of 28 are: $$ 28, 56, 84, 112, 140, \ldots $$
- Identify the common multiples
Next, we will look for any common multiples in the lists we created. From the multiples of 21 and 28, we can see that:
- The common multiples identified are: $$ 84, \ldots $$
- Determine the least common multiple
The least common multiple is the smallest number that appears in both lists. In this case, the smallest common multiple is:
$$ \text{LCM}(21, 28) = 84 $$
The least common multiple of 21 and 28 is $84$.
More Information
The least common multiple (LCM) is important in various mathematical applications, such as simplifying fractions, adding fractions with different denominators, and solving problems involving ratios.
Tips
- Ignoring higher multiples: Sometimes, students might assume that the first number they find that appears in both lists is the answer without verifying it is the least one.
- Mistaking GCD for LCM: Remember that greatest common divisor (GCD) is different from LCM; they serve different purposes in math.
