Math Problem Statement
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:
-
Prime factorization of each number:
- is already a prime number.
- is also a prime number.
- .
- .
-
Take the highest power of each prime factor from the factorizations:
- For 3: The highest power is .
- For 5: The highest power is .
- For 2: The highest power is .
-
Multiply these highest powers:
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:
- What is the difference between LCM and GCD (Greatest Common Divisor)?
- How can you find the LCM using a different method like listing multiples?
- What is the LCM of three numbers: 8, 12, and 20?
- Can LCM be smaller than any of the numbers given?
- 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