Find the L.C.D. of the following group of fractions and express in terms of the L.C.D.

1/3, 3/5, 21/25,13/15
Puzzle!

3 = 3

5 = 5
25 = 5*5
15 = 3*5
so we need two fives and one three
5*5*3 = 75

There are several ways to approach this problem. I like finding the multiples of the largest number and then finding the one that all of the denominators will go into.

Example:
25, 50, 75, 100, 125

1/3 = ?/75

25/75

3/5 = ?/75
multiply top and bottom by 15
45/75

21/25 = ?/75
top and bottom by 3
63/75

13/15 = ?/75
top and bottom by 5
13*5 = 65
65/75

To find the LCD (Least Common Denominator) of a group of fractions, you need to find the smallest multiple that all the denominators have in common. Here's how you can do it step by step:

Step 1: Identify the denominators of each fraction:
The denominators of the given fractions are 3, 5, 25, and 15.

Step 2: Determine the prime factors of each denominator:
Prime factorization is the process of breaking down a number into its prime factors (the smallest prime numbers that multiply together to give the original number).

The prime factors of the denominators are:
- 3 = 3 (prime factor)
- 5 = 5 (prime factor)
- 25 = 5 * 5 (prime factors)
- 15 = 3 * 5 (prime factors)

Step 3: Identify the highest power of each prime factor:
From the prime factorizations, we can see that the highest power of 3 is 3^1 and the highest power of 5 is 5^2.

Step 4: Calculate the product of the highest powers of the prime factors:
Multiply the highest power of each prime factor together:
3^1 * 5^2 = 3 * 25 = 75

The Least Common Denominator (LCD) of the given group of fractions is 75.