What is the least common multiple of 10 and 2?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 10 and 2, which is the smallest number that both 10 and 2 can divide into without leaving a remainder. To find the LCM, we will list the multiples of each number and identify the smallest common one.
Answer
10
Answer for screen readers
The final answer is 10
Steps to Solve
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List the multiples of each number
List the first few multiples of 10 and 2:
- Multiples of 10: 10, 20, 30, 40, 50, ...
- Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...
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Identify the smallest common multiple
Find the first common multiple in both lists:
- The smallest common multiple is 10.
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Verify by division
Ensure that the smallest common multiple can be divided by both original numbers without a remainder: $$egin{aligned} 10 \div 10 &= 1 \ 10 \div 2 &= 5 \ ext{(no remainders)} \end{aligned}$$
The final answer is 10
More Information
The LCM is useful in many mathematical contexts, including finding common denominators and solving problems involving intervals.
Tips
A common mistake is forgetting to list enough multiples or overlooking the first common multiple. To avoid this, write out a few more multiples of each number if needed.
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