Math Problem Statement
Which statement is true? Group of answer choices
The least common multiple of 4 and 8 is 16.
The least common multiple of 6 and 10 is 30
The least common multiple of 4 and 10 is 40.
The least common multiple of 6 and 8 is 48.
Solution
Let's evaluate the least common multiples (LCM) for each pair of numbers:
-
LCM of 4 and 8: The factors of 4 are and the factors of 8 are . The LCM takes the highest power of all prime factors, so the LCM is .
This statement is false (LCM is 8, not 16). -
LCM of 6 and 10: The factors of 6 are and the factors of 10 are . The LCM is found by taking the highest power of each prime factor:
.
This statement is true. -
LCM of 4 and 10: The factors of 4 are and the factors of 10 are . The LCM is .
This statement is false (LCM is 20, not 40). -
LCM of 6 and 8: The factors of 6 are and the factors of 8 are . The LCM is .
This statement is false (LCM is 24, not 48).
Conclusion:
The true statement is:
The least common multiple of 6 and 10 is 30.
Would you like any further details or explanations?
Here are 5 relative questions to expand this concept:
- How do you find the greatest common divisor (GCD) of two numbers?
- What is the relationship between GCD and LCM for two numbers?
- How do you calculate the LCM of three numbers?
- What are prime factorization and its role in finding the LCM?
- Can the LCM of two numbers ever be smaller than one of the numbers?
Tip: The LCM of two numbers is always greater than or equal to the larger number.
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Math Problem Analysis
Mathematical Concepts
Least Common Multiple (LCM)
Prime Factorization
Multiples
Formulas
LCM formula: Use the highest powers of all prime factors
Theorems
Prime Factorization Theorem
Suitable Grade Level
Grades 6-8