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 Least Common Multiple (LCM) of fractions using a TI-84 calculator, follow these steps:

Step 1: Identify the fractions

Let’s say we have two fractions, such as:
[
\frac{a}{b} \quad \text{and} \quad \frac{c}{d}
]
where (a), (b), (c), and (d) are integers, and you wish to find the LCM of these fractions.

Step 2: Find the LCM of the numerators

The first thing to do is calculate the LCM of the numerators, (a) and (c). To do this:

1. Press the MATH button.
2. Select 9: lcm(.
3. Enter the numerators, separated by a comma. For example, if the fractions are ( \frac{4}{5} ) and ( \frac{6}{7} ), you would enter 4,6.
4. Press ENTER.

This will give you the LCM of the numerators.

Step 3: Find the GCD of the denominators

Next, find the greatest common divisor (GCD) of the denominators (b) and (d). The formula for finding the LCM of the fractions requires the GCD of the denominators. To calculate the GCD on the TI-84:

1. Press the MATH button.
2. Choose 2: gcd(.
3. Enter the denominators separated by a comma, such as 5,7 for the fractions ( \frac{4}{5} ) and ( \frac{6}{7} ).
4. Press ENTER.

Step 4: Calculate the LCM of the fractions

Now, apply the formula for the LCM of two fractions:
[
\text{LCM of fractions} = \frac{\text{LCM of the numerators}}{\text{GCD of the denominators}}
]
You already have the LCM of the numerators and the GCD of the denominators, so simply divide the results:

1. Take the result of the LCM of the numerators.
2. Divide it by the result of the GCD of the denominators.
3. This will give you the LCM of the fractions.

Example Calculation

For the fractions ( \frac{4}{5} ) and ( \frac{6}{7} ):

1. LCM of Numerators: LCM(4, 6) = 12
2. GCD of Denominators: GCD(5, 7) = 1
3. LCM of Fractions: ( \frac{12}{1} = 12 )

Thus, the LCM of ( \frac{4}{5} ) and ( \frac{6}{7} ) is 12.

This process can be extended to more fractions by repeating the steps above. By following these steps on the TI-84, you can efficiently find the LCM of any set of fractions.