Math Problem Statement

Find the least common multiple (LCM) of 3, 5, 10, and 25.

Solution

The image provided is a quiz question, which appears to ask for the least common multiple (LCM) of the numbers 3, 5, 10, and 25. I'll solve it for you:

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

  1. Prime factorization of each number:

    • 33 is already a prime number.
    • 55 is also a prime number.
    • 10=2×510 = 2 \times 5.
    • 25=5225 = 5^2.
  2. Take the highest power of each prime factor from the factorizations:

    • For 3: The highest power is 313^1.
    • For 5: The highest power is 525^2.
    • For 2: The highest power is 212^1.
  3. Multiply these highest powers: LCM=31×52×21=3×25×2=150.LCM = 3^1 \times 5^2 \times 2^1 = 3 \times 25 \times 2 = 150.

So, the least common multiple of 3, 5, 10, and 25 is 150.

Would you like more details or have any other questions?

Here are five related questions you could explore:

  1. What is the difference between LCM and GCD (Greatest Common Divisor)?
  2. How can you find the LCM using a different method like listing multiples?
  3. What is the LCM of three numbers: 8, 12, and 20?
  4. Can LCM be smaller than any of the numbers given?
  5. How does LCM apply to real-world problems like scheduling or synchronization?

Tip: When working with prime factorization, always ensure to include the highest powers of all primes involved for accurate LCM results.

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Math Problem Analysis

Mathematical Concepts

Number Theory
Prime Factorization
Least Common Multiple (LCM)

Formulas

LCM(a, b, c, ...) = product of the highest powers of prime factors

Theorems

Prime Factorization Theorem
LCM Theorem

Suitable Grade Level

Grades 6-9