lcm of 10 and 35
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 10 and 35. To solve this, we will find the multiples of both numbers and determine the smallest multiple that they share.
Answer
The least common multiple of 10 and 35 is $70$.
Answer for screen readers
The least common multiple (LCM) of 10 and 35 is $70$.
Steps to Solve
- Identify the multiples of each number
Start by listing a few multiples of 10 and 35.
For 10:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, ...
For 35:
35, 70, 105, 140, 175, 210, ...
- Find the common multiples
Look through the lists of multiples to find the ones that appear in both lists.
From the lists above, we see that 70 is the first number that appears in both.
- Determine the least common multiple (LCM)
The least common multiple is the smallest number that is common to both lists of multiples. Since 70 is the first common multiple, it is the LCM of 10 and 35.
The least common multiple (LCM) of 10 and 35 is $70$.
More Information
The least common multiple is used in various applications, such as adding fractions with different denominators. Knowing the LCM can simplify these operations and make calculations easier.
Tips
- Forgetting to list enough multiples, which could lead to overlooking the smallest common multiple.
- Stopping the process too early after finding a common multiple without verifying if it's the least one.
