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The question asks for the least common multiple (LCM) of 18, 29, and 27.

To find the LCM of these numbers, follow these steps:

1. **Prime Factorization**:
   - \( 18 = 2 \times 3^2 \)
   - \( 29 \) is a prime number.
   - \( 27 = 3^3 \)

2. **Determine the highest powers of each prime factor**:
   - For 2: the highest power is \( 2^1 \) (from 18).
   - For 3: the highest power is \( 3^3 \) (from 27).
   - For 29: the highest power is \( 29^1 \) (since 29 is prime).

3. **Multiply the highest powers together**:
   - \( LCM = 2^1 \times 3^3 \times 29^1 \)
   - \( = 2 \times 27 \times 29 \)
   - \( = 2 \times 783 = 1566 \)

So, the least common multiple of 18, 29, and 27 is **1566**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the greatest common divisor (GCD) of numbers?
2. What are the prime factors of 72, and how do they relate to LCM?
3. Can LCM and GCD be found using a Venn diagram of prime factors?
4. How is the LCM used in adding or subtracting fractions?
5. What is the difference between LCM and HCF?

**Tip**: Always find the LCM by identifying the highest powers of all primes in the factorization!

What is the least common multiple of 18, 29, and 27?

Learn how to find the least common multiple (LCM) of 18, 29, and 27 using prime factorization. This problem involves key number theory concepts like prime factorization and LCM calculation. Suitable for students in Grades 6-8.

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