How to Find the Least Common Denominator
List the multiples of each denominator., Identify the lowest common multiple., Rewrite the original equation., Solve the rewritten problem.
Step-by-Step Guide
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Step 1: List the multiples of each denominator.
Make a list of several multiples for each denominator in the equation.
Each list should consist of the denominator numeral multiplied by 1, 2, 3, 4, and so on.
Example: 1/2 + 1/3 + 1/5 Multiples of 2: 2 * 1 = 2; 2 * 2 = 4; 2 * 3 = 6; 2 * 4 = 8; 2 * 5 = 10; 2 * 6 = 12; 2 * 7 = 14; etc.
Multiples of 3: 3 * 1 = 3; 3 * 2 = 6; 3 *3 = 9; 3 * 4 = 12; 3 * 5 = 15; 3 * 6 = 18; 3 * 7 = 21; etc.
Multiples of 5: 5 * 1 = 5; 5 * 2 = 10; 5 * 3 = 15; 5 * 4 = 20; 5 * 5 = 25; 5 * 6 = 30; 5 * 7 = 35; etc. -
Step 2: Identify the lowest common multiple.
Scan through each list and mark any multiples that are shared by all of the original denominators.
After identifying the common multiples, identify the lowest denominator.
Note that if no common denominator exists at this point, you may need to continue writing out multiples until you eventually come across a shared multiple.
This method is easier to use when small numbers are present in the denominator.
In this example, the denominators only share one multiple and it is 30: 2 * 15 = 30; 3 * 10 = 30; 5 * 6 = 30 The LCD = 30 , In order to change each fraction in the equation so that it remains true to the original equation, you will need to multiply each numerator (the top of the fraction) and denominator by the same factor used to multiply the corresponding denominator when reaching the LCD.
Example: (15/15) * (1/2); (10/10) * (1/3); (6/6) * (1/5) New equation: 15/30 + 10/30 + 6/30 , After finding the LCD and changing the fractions accordingly, you should be able to solve the problem without further difficulty.
Remember to simplify the fraction at the end.
Example: 15/30 + 10/30 + 6/30 = 31/30 = 1 1/30 -
Step 3: Rewrite the original equation.
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Step 4: Solve the rewritten problem.
Detailed Guide
Make a list of several multiples for each denominator in the equation.
Each list should consist of the denominator numeral multiplied by 1, 2, 3, 4, and so on.
Example: 1/2 + 1/3 + 1/5 Multiples of 2: 2 * 1 = 2; 2 * 2 = 4; 2 * 3 = 6; 2 * 4 = 8; 2 * 5 = 10; 2 * 6 = 12; 2 * 7 = 14; etc.
Multiples of 3: 3 * 1 = 3; 3 * 2 = 6; 3 *3 = 9; 3 * 4 = 12; 3 * 5 = 15; 3 * 6 = 18; 3 * 7 = 21; etc.
Multiples of 5: 5 * 1 = 5; 5 * 2 = 10; 5 * 3 = 15; 5 * 4 = 20; 5 * 5 = 25; 5 * 6 = 30; 5 * 7 = 35; etc.
Scan through each list and mark any multiples that are shared by all of the original denominators.
After identifying the common multiples, identify the lowest denominator.
Note that if no common denominator exists at this point, you may need to continue writing out multiples until you eventually come across a shared multiple.
This method is easier to use when small numbers are present in the denominator.
In this example, the denominators only share one multiple and it is 30: 2 * 15 = 30; 3 * 10 = 30; 5 * 6 = 30 The LCD = 30 , In order to change each fraction in the equation so that it remains true to the original equation, you will need to multiply each numerator (the top of the fraction) and denominator by the same factor used to multiply the corresponding denominator when reaching the LCD.
Example: (15/15) * (1/2); (10/10) * (1/3); (6/6) * (1/5) New equation: 15/30 + 10/30 + 6/30 , After finding the LCD and changing the fractions accordingly, you should be able to solve the problem without further difficulty.
Remember to simplify the fraction at the end.
Example: 15/30 + 10/30 + 6/30 = 31/30 = 1 1/30
About the Author
James Hayes
Experienced content creator specializing in lifestyle guides and tutorials.
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