LCM of 3, 5, and 9
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 3, 5, and 9. To find the LCM, we need to determine the smallest multiple that is common to all three numbers.
Answer
The least common multiple (LCM) of 3, 5, and 9 is $45$.
Answer for screen readers
The least common multiple (LCM) of 3, 5, and 9 is $45$.
Steps to Solve
- List the multiples Start by listing some of the multiples for each of the numbers.
Multiples of 3: $$3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...$$
Multiples of 5: $$5, 10, 15, 20, 25, 30, 35, ...$$
Multiples of 9: $$9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...$$
- Identify common multiples Next, determine which multiples are common to all three lists.
From the lists:
- Common multiples of 3 and 5 include: 15, 30, ...
- Common multiples including 9 must also be checked.
- Find the smallest common multiple Look for the smallest number that appears in all three lists of multiples.
The smallest common multiple found in the lists is $45$.
- Verify the result To ensure that 45 is indeed the LCM, we can check if it is divisible by all three numbers:
- $45 \div 3 = 15$ (divisible)
- $45 \div 5 = 9$ (divisible)
- $45 \div 9 = 5$ (divisible)
Since all checks are valid, $45$ is confirmed as the least common multiple.
The least common multiple (LCM) of 3, 5, and 9 is $45$.
More Information
The least common multiple is essential in various applications, such as finding a common time for events and simplifying fractions. The LCM can be calculated using prime factorization methods, where you express each number in terms of its prime factors and choose the highest power for each prime in the calculations.
Tips
- Forgetting to list enough multiples, which may lead to missing the LCM.
- Not verifying that the identified LCM is divisible by all original numbers.
