When you see '3x 5 11', what comes to mind? For many, it might immediately trigger thoughts of mathematical problems, perhaps a quiz question or a snippet from a textbook. And indeed, the reference material points us directly to the realm of elementary mathematics, specifically focusing on the concept of the Least Common Multiple (LCM).
Let's dive into that. The question posed in the reference documents is straightforward: "What is the least common multiple of 3, 5, and 11?" The answer, as explained, hinges on understanding how to find the LCM. The key insight here is that 3, 5, and 11 are what we call 'coprime' numbers. This means they don't share any common factors other than 1. When numbers are coprime, their least common multiple is simply their product.
So, we calculate 3 multiplied by 5, which gives us 15. Then, we multiply that result by 11. 15 times 11 equals 165. This is why option B, 165, is the correct answer. The explanation emphasizes that the LCM is the product of common prime factors and unique prime factors. Since 3, 5, and 11 are all unique prime factors (and also coprime), their product is indeed their LCM.
But '3x 5 11' can also appear in a different context, as seen in Reference Document 3 and 4. Here, it's part of an algebraic equation: '3x + 5 = 11'. This is a simple linear equation, a fundamental building block in algebra. To solve for 'x', we use basic algebraic operations. First, we isolate the term with 'x' by subtracting 5 from both sides of the equation: 3x + 5 - 5 = 11 - 5, which simplifies to 3x = 6. Then, to find the value of 'x', we divide both sides by 3: 3x / 3 = 6 / 3, giving us x = 2. This solution, x=2, is then used in further problems, such as determining the value of 'a' in another equation where this 'x=2' must also be a solution.
It's fascinating how a simple sequence of numbers and symbols can represent such different mathematical concepts. Whether it's finding the smallest number divisible by a set of numbers (LCM) or solving for an unknown variable in an equation, '3x 5 11' serves as a versatile example. It reminds us that numbers are not just abstract symbols but tools that help us understand and solve problems in various aspects of mathematics, from basic arithmetic to more complex algebra.
