Math Problem Statement
What are th lowest common multiples?(a) 2 and 17 (b) 7 and 5 (c) 9 and 12 (d) 24f and 18f^2
Solution
The lowest common multiple (LCM) of two or more numbers is the smallest number that is a multiple of each of them.
Here are the calculations for the given pairs:
(a) 2 and 17
- Prime factors of 2:
- Prime factors of 17:
- Since 2 and 17 are coprime (no common factors), the LCM is their product:
(b) 7 and 5
- Prime factors of 7:
- Prime factors of 5:
- Since 7 and 5 are coprime, the LCM is their product:
(c) 9 and 12
- Prime factorization:
- The LCM takes the highest power of each prime factor:
- (from 9)
- (from 12)
- LCM:
(d) 24f and 18f²
- Prime factorization:
- The LCM takes the highest power of each factor:
- (from 24f)
- (from 18f²)
- (from 18f²)
- LCM:
Final Results:
- (a)
- (b)
- (c)
- (d)
Do you want more detailed steps or have any questions? Here are 5 related questions to explore further:
- What is the difference between LCM and greatest common divisor (GCD)?
- How is the LCM used in solving equations with fractions?
- How can the LCM be calculated using the Euclidean algorithm?
- What are some real-life applications of LCM in scheduling problems?
- Can you find the LCM of more than two numbers simultaneously?
Tip: For polynomials, the LCM includes the highest powers of each variable and factor.
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Math Problem Analysis
Mathematical Concepts
Lowest Common Multiple (LCM)
Prime Factorization
Multiples
Formulas
LCM(a, b) = (a × b) / GCD(a, b)
LCM includes the highest powers of all prime factors involved
Theorems
Fundamental Theorem of Arithmetic (every integer > 1 can be uniquely factorized into prime numbers)
Suitable Grade Level
Grades 6-8