how to use TI-84 calculator to find the lcm of fractions

how to use TI-84 calculator to find the lcm of fractions

The correct answer and explanation is:

To find the LCM (Least Common Multiple) of fractions using a TI-84 calculator, you must first understand a key concept:

🧠 LCM of Fractions Formula:

LCM of fractions=LCM of numeratorsGCD of denominators\text{LCM of fractions} = \frac{\text{LCM of numerators}}{\text{GCD of denominators}}

So, you don’t find the LCM of the fractions directly; you instead:

• Find the LCM of the numerators
• Find the GCD (Greatest Common Divisor) of the denominators
• Divide the LCM of the numerators by the GCD of the denominators

✅ Steps on the TI-84 Calculator:

Example: Find the LCM of 34\frac{3}{4} and 56\frac{5}{6}

Step 1: Find LCM of Numerators (3 and 5)

1. Press MATH
2. Scroll right to NUM
3. Select 8: lcm( and press ENTER
4. Input 3,5 and press ENTER
   • You should get: 15

Step 2: Find GCD of Denominators (4 and 6)

1. Press MATH
2. Scroll right to NUM
3. Select 9: gcd( and press ENTER
4. Input 4,6 and press ENTER
   • You should get: 2

Step 3: Divide the Results

Now divide the LCM of the numerators by the GCD of the denominators:

1. Type 15 ÷ 2 and press ENTER
   • You get: 7.5 or as a fraction: 152\frac{15}{2}

📘 Explanation (300 words):

The Least Common Multiple (LCM) of fractions is not a common operation directly supported on the TI-84 calculator, so we use a mathematical shortcut: instead of trying to find a multiple of entire fractions, we compute the LCM of their numerators and the GCD of their denominators. This gives us a single fraction that is a common multiple of the two original ones.

In our example, the LCM of 3 and 5 is 15, because 15 is the smallest number both 3 and 5 divide into. The GCD of 4 and 6 is 2, since 2 is the largest number that divides both. Dividing 15 by 2 gives 152\frac{15}{2}, which is the least common multiple of the fractions 34\frac{3}{4} and 56\frac{5}{6}.

This method works for any fractions. Always remember to:

1. Find LCM of the numerators
2. Find GCD of the denominators
3. Divide the two values

By using the lcm( and gcd( functions in the TI-84’s MATH → NUM menu, you efficiently compute this without manual effort. This is a fast and accurate method that supports solving problems in algebra, arithmetic, and real-world applications.