Lowest Common Denominator Lowest Common Denominator The Lowest Common Denominator in mathematics is the least common multiple of 2 or more denominators of a number of fractions or we can say that Lowest Common Denominator is the smallest of the positive integers which are the multiple of the denominators. lowest common denominator in short form is written as LCD. Now, we will get to know more about the term ‘least common multiple ‘. Before understanding the meaning of the term least common multiple, it is first necessary to know that what is the meaning of a ‘multiple ‘. The multiple of any no. is some whole no. times of that no.. Let us take an example. Let us take any number, say 4 then some of the multiples of 4 are 4, 8, 12, 16, 20 and 24. Now, if we have to find the Lowest Common Denominator of 2 fractions, first we have to find the common multiples of their denominators. The common multiple of any 2 numbers is a number which is a multiple of both of them.
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The lowest or the smallest multiple of all those common multiples of those 2 numbers is known as the ‘least common multiple ‘. This least common multiple of the denominators of any 2 fractions is called the Lowest Common Denominator of those 2 fractions. Let us take an example, say we have to find the least common multiple of 5 and 7. To solve this problem in most easy way, we will write some of the multiples of each number and then see the smallest common number of the 2 lists. Multiples of 5 are- 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, … Multiples of 7 are- 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, … In the two lists, we observe that both the numbers 35 and 70 are the common multiples of 5 and 7 but the smallest of them is the least common multiple which is 35 here. Let us see another procedure to find the Lowest Common Denominator. To calculate the Lowest Common Denominator of any 2 fractions, first we have to get the greatest of the common factors of the denominators of the fractions. Then, we have to do the multiplication of all the denominators. After doing this step, we have to divide the result of the multiplication of the denominators by the greatest of the common factor found in first step to get the Lowest Common Denominator. Also, we can find the Lowest Common Denominator by dividing any one of the denominators by the greatest of the common factor and then multiplying their quotient with the other denominator.
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Let us take another example, say we have to calculate the Lowest Common Denominator of 3/8 and 5/12. To get the Lowest Common Denominator of these 2 fractions, first we calculate the greatest of the common factors of the denominators 8 and 12 which comes out to be 4 here. Then we either do the multiplication of the denominators and divide the result of the multiplication by the greatest of the common factor to get the Lowest Common Denominator, i.e., 8 * 12 = 96 and 96/4 = 24 which is the Lowest Common Denominator.
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