To find the least common multiple (LCM) of 33, 45, and 99, we can use the prime factorization method:

1. **Prime factorization of 33:**
   \[
   33 = 3 \times 11
   \]

2. **Prime factorization of 45:**
   \[
   45 = 3^2 \times 5
   \]

3. **Prime factorization of 99:**
   \[
   99 = 3^2 \times 11
   \]

The LCM is found by taking the highest power of each prime number that appears in any of the factorizations:

- **3:** The highest power is \(3^2\) (from 45 and 99).
- **11:** The highest power is \(11^1\) (from 33 and 99).
- **5:** The highest power is \(5^1\) (from 45).

Now, multiply the highest powers together:

\[
LCM = 3^2 \times 11 \times 5 = 9 \times 11 \times 5 = 99 \times 5 = 495
\]

So, the LCM of 33, 45, and 99 is **495**.

Would you like more details or have any other questions?

Here are 5 related questions:
1. How do you find the LCM using the division method?
2. What is the difference between LCM and GCD?
3. How would you find the LCM of three numbers using a Venn diagram?
4. How is LCM applied in solving real-life problems involving time and schedules?
5. Can you find the LCM of numbers that include variables (e.g., algebraic expressions)?

**Tip:** When finding the LCM, always look for the highest powers of the prime factors involved to ensure accuracy.

Learn how to find the least common multiple (LCM) of 33, 45, and 99 using the prime factorization method. This step-by-step solution covers key concepts like prime factorization and finding the highest powers of factors. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation