Math Problem Statement
Work out the lowest common multiple (LCM) of 8 and 10.
Solution
The task asks for the Lowest Common Multiple (LCM) of 8 and 10. Let's work through the solution step-by-step.
Steps to find the LCM of 8 and 10:
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Prime Factorization:
- 8 = 2 × 2 × 2
- 10 = 2 × 5
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Take the highest powers of all prime factors:
- The primes involved are 2 and 5.
- The highest power of 2 is (from 8).
- The highest power of 5 is (from 10).
-
Multiply these highest powers:
Thus, the LCM of 8 and 10 is 40.
Do you need any further clarification, or have any other questions about LCM? Here are some related questions for you:
- How do we find the Greatest Common Divisor (GCD) of two numbers?
- What is the LCM of 12 and 15?
- How do we use prime factorization to calculate the LCM?
- How can LCM be used in real-life applications?
- Can the LCM be smaller than one of the numbers? Explain why or why not.
Tip: When calculating the LCM using prime factorization, always ensure to include every prime factor involved, using the highest exponent from both numbers.
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Math Problem Analysis
Mathematical Concepts
LCM
Prime Factorization
Formulas
LCM(a, b) = (a × b) / GCD(a, b)
Theorems
Fundamental Theorem of Arithmetic (Prime Factorization)
Suitable Grade Level
Grade 6-8