Prepare for Least Common Denominator
LCD is the lowest common denominator. Least common denominator,(LCD) is the least common multiples of all the denominators of a set of fractions. It is the smallest positive number get from multiples of all the denominators. The lowest common denominator is useful for complicated problems of addition, subtraction in easy way. Also useful for comparing the fractions. The lowest common multiple of and is written as LCM (l, m). Lowest common multiple can be divided by the two numbers (fractional denominator) without remainder.
Steps and methods to prepare for least common denominator
There are the following steps to find the lowest common multiple(lcm).
There are two methods for finding the LCD
List the multiples
Examples – prepare for least common denominator
Prepare for least common denominator - Example 1
Problem 1: calculate the LCM for the given numbers 24, 12 by list of multiples method
Solution: First step is to compute the list of multiples
The multiples of 24 is 24, 48, 72, 96
The multiples of 12 are 12, 24, 36, 48.
The lowest common denominator for 12, 24 is 24.
Prepare for least common denominator - Example 2
Problem 2: Calculate the value for the given number `2/25 + 5/75` .
Solution: The factor of 25 is 5 x 5.
The factors of 75 is 5 x 5 x 3
The lowest common denominator of 25 and 75 are `5*5*3` = 75
Therefore lcm is 75.
The value of `2/25 + 5/75 = (6+5)/75 = 11/75`
Practice problems – prepare for least common denominator
Problem 1: Calculate the LCM for the given numbers 24, 36
Answer: Lowest common multiple is 72
Problem 2: Find the result for the given numbers `1/3+23/22`
Answer : The result is `91/66` .
Steps and methods to prepare for least common denominator
There are the following steps to find the lowest common multiple(lcm).
- Compute the factors of the number (the number may be two or three)
- Example is the multiple of 6 and 8 is 2, 3, 6 for 6 and 2, 4, 8 for 8. The lowest common multiple is 2 x 3 x 4 = 24
There are two methods for finding the LCD
- List the multiples
- Factor each of the denominators
List the multiples
- To find the least common denominator, just list the multiples of each denominator (multiply by 2, 3, 4, etc.) and then choose the smallest number that appears in each list.
- To find the least common denominator using the second method, first factor each of the denominators into primes. Then multiply each different prime number in all of the factorization.
Examples – prepare for least common denominator
Prepare for least common denominator - Example 1
Problem 1: calculate the LCM for the given numbers 24, 12 by list of multiples method
Solution: First step is to compute the list of multiples
The multiples of 24 is 24, 48, 72, 96
The multiples of 12 are 12, 24, 36, 48.
The lowest common denominator for 12, 24 is 24.
Prepare for least common denominator - Example 2
Problem 2: Calculate the value for the given number `2/25 + 5/75` .
Solution: The factor of 25 is 5 x 5.
The factors of 75 is 5 x 5 x 3
The lowest common denominator of 25 and 75 are `5*5*3` = 75
Therefore lcm is 75.
The value of `2/25 + 5/75 = (6+5)/75 = 11/75`
Practice problems – prepare for least common denominator
Problem 1: Calculate the LCM for the given numbers 24, 36
Answer: Lowest common multiple is 72
Problem 2: Find the result for the given numbers `1/3+23/22`
Answer : The result is `91/66` .