Solution: We compute $ \frac{3}{8} + \frac{5}{12} + \frac{7}{16} $. The least common denominator of 8, 12, and 16 is 48. Convert each fraction:

["How to Compute $ \frac{3}{8} + \frac{5}{12} + \frac{7}{16} $: A Step-by-Step Guide Using the Least Common Denominator", "When adding fractions, one of the most essential steps is finding a common denominator — and in this case, the least common denominator (LCD) plays a key role in simplifying the math. In this article, we’ll walk through how to compute $ \frac{3}{8} + \frac{5}{12} + \frac{7}{16} $ using the LCD of 8, 12, and 16, which is 48.", "---", "### Why Find a Common Denominator?", "Fractions represent parts of a whole, and when they represent parts of different sizes, direct addition isn’t possible unless they’re converted to similar portions. The least common denominator ensures each fraction is expressed in terms of equal-sized parts — making addition accurate and straightforward.", "---", "### Step 1: Identify the Least Common Denominator", "We are working with denominators: 8, 12, and 16. To find the least common denominator:", "- Prime factorization:\n - 8 = $ 2^3 $\n - 12 = $ 2^2 \ imes 3 $\n - 16 = $ 2^4 $", "The LCD takes the highest power of each prime factor:\n- $ 2^4 = 16 $\n- $ 3 $", "So, $ \ ext{LCD} = 16 \ imes 3 = 48 $", "---", "### Step 2: Convert Each Fraction to an Equivalent with Denominator 48", "Now convert each fraction to an equivalent with denominator 48:", "#### $\frac{3}{8}$\nFind what we multiply 8 by to get 48:\n$ 48 \div 8 = 6 $\nMultiply numerator and denominator by 6:\n$$\n\frac{3}{8} = \frac{3 \ imes 6}{8 \ imes 6} = \frac{18}{48}\n$$", "#### $\frac{5}{12}$\nFind what we multiply 12 by:\n$ 48 \div 12 = 4 $\n$$\n\frac{5}{12} = \frac{5 \ imes 4}{12 \ imes 4} = \frac{20}{48}\n$$", "#### $\frac{7}{16}$\nFind what we multiply 16 by:\n$ 48 \div 16 = 3 $\n$$\n\frac{7}{16} = \frac{7 \ imes 3}{16 \ imes 3} = \frac{21}{48}\n$$", "---", "### Step 3: Add the Equivalent Fractions", "Now add the numerators over the common denominator:", "$$\n\frac{18}{48} + \frac{20}{48} + \frac{21}{48} = \frac{18 + 20 + 21}{48} = \frac{59}{48}\n$$", "---", "### Final Result", "The sum is $ \frac{59}{48} $, which is an improper fraction — meaning it’s greater than one. As a mixed number, this is $ 1 \frac{11}{48} $.", "---", "### Summary", "Adding fractions becomes simple when you use the least common denominator. Here’s a quick recap:", "- LCD of 8, 12, 16 is 48\n- Convert: $ \frac{3}{8} = \frac{18}{48} $, $ \frac{5}{12} = \frac{20}{48} $, $ \frac{7}{16} = \frac{21}{48} $\n- Add: $ \frac{18 + 20 + 21}{48} = \frac{59}{48} $", "Using the LCD ensures accuracy and clarity in arithmetic with fractions — a vital skill in math, science, and everyday problem-solving.", "---", "Keywords: add fractions, compute $ \frac{3}{8} + \frac{5}{12} + \frac{7}{16} $, least common denominator, LCD 48, fractions simplification, math tutorial."]