least common multiple of 10 and 7
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 10 and 7. To find the LCM, we can use the prime factorization method or the multiplication method to identify the smallest number that is a multiple of both 10 and 7.
Answer
The least common multiple of 10 and 7 is $70$.
Answer for screen readers
The least common multiple of 10 and 7 is $70$.
Steps to Solve
- List the multiples of each number
Start by listing a few multiples of both numbers to identify the least common multiple.
- Multiples of 10: 10, 20, 30, 40, 50, 60, 70, ...
- Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, ...
- Identify the smallest common multiple
From the lists of multiples, find the smallest number that appears in both lists.
In this case, the first common multiple is 70.
- Conclusion
The least common multiple of 10 and 7 is:
$$ \text{LCM}(10, 7) = 70 $$
The least common multiple of 10 and 7 is $70$.
More Information
The least common multiple (LCM) is the smallest number that is a multiple of both given numbers. In this case, $70$ is the first number that both $10$ and $7$ can divide evenly without a remainder.
Tips
- Confusing the LCM with the greatest common divisor (GCD); remember that LCM finds the smallest number common to both sets of multiples, while GCD finds the largest number that divides both numbers.
- Not listing enough multiples; sometimes the LCM can be larger than the first few multiples, so it is important to check enough values.
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