Math Problem Statement
Find the least common multiple of 3 and 14.
Solution
To find the least common multiple (LCM) of 3 and 14, we can follow these steps:
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List the prime factors:
- 3 is a prime number, so its prime factorization is .
- 14 can be factored as .
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Identify the highest powers of each prime factor:
- The factors are 2, 3, and 7.
- The highest powers are: , , and .
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Multiply these together:
Thus, the least common multiple of 3 and 14 is 42.
Would you like more details, or do you have any questions?
Here are 5 related questions:
- What is the LCM of 6 and 14?
- How do you find the greatest common divisor (GCD) of two numbers?
- Can you explain the relationship between LCM and GCD?
- How is the LCM of two prime numbers calculated?
- What are the properties of multiples in number theory?
Tip: The LCM of two numbers is always a multiple of their greatest common divisor (GCD).
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Math Problem Analysis
Mathematical Concepts
Number Theory
Prime Factorization
Least Common Multiple (LCM)
Formulas
LCM(a, b) = (a * b) / GCD(a, b)
Prime factorization
Theorems
Fundamental Theorem of Arithmetic
Suitable Grade Level
Grades 5-7