Math Problem Statement
Solution
The problem in the image asks to find the smallest integer such that:
This means that must be divisible by the consecutive primes starting from 2 up to 23. Essentially, we are asked to find the least common multiple (LCM) of these primes.
The primes involved are: 2, 3, 5, 7, 11, 13, 17, 19, and 23.
Thus, the smallest possible value of will be the least common multiple of these primes:
Since these are distinct prime numbers, the LCM is simply the product of all the primes:
Let me compute this for you:
Therefore, the smallest possible value of that satisfies all the given conditions is .
Would you like further details or clarifications on this solution?
Here are 5 related questions you might find helpful:
- What is the significance of the least common multiple in problems like this?
- How do you compute the LCM for a set of numbers in general?
- Can this type of problem be solved using other methods like the Chinese Remainder Theorem?
- What happens if non-prime numbers are included in the conditions?
- How would the solution change if one of the primes were excluded?
Tip: When solving problems involving divisibility by several primes, finding the LCM is a straightforward and efficient method to get the smallest solution.
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Math Problem Analysis
Mathematical Concepts
Number Theory
Modular Arithmetic
Least Common Multiple
Formulas
n = LCM(2, 3, 5, 7, 11, 13, 17, 19, 23)
Theorems
Prime Factorization
Least Common Multiple
Suitable Grade Level
Grades 10-12