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Common denominator of 9 4 11 5

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4 Answers

Finding the LCM (Least Common Multiple) of a list of numbers, using Prime Factorization.

Step 1 Write the prime factorization of each number.

Step 2 For each factor that's different from the prime in step 1, circle the largest number of the factors found in any one factorization

4=2x2

5=5x1

9=3x3

11=1x11

=2x2x5x3x3x11

=1980

9 = 3 * 3

4 = 2 * 2

11 is prime

5 is prime

The answer is 3 * 3 * 2 * 2 * 11 * 5 = 36 * 55 = 1980 (no shared factors between numbers).

Ashley,

If you listed the fractions with your question, I am not seeing them.  So I will give a generic answer to this question.  Assuming that the numbers you provided which are 9, 11, 4 and 5 are all denominators of fractions, their common denominator will be 9*4*5*11 because none of those numbers have any factors that are shared

The factors for 9 are 3 and 3, the factors for 4 are 2 and 2 and the other two numbers 11 and 5 are prime numbers and therefore have no factors.  9 and 4, the only numbers with factors do not have shared factors, the common denominator is the product of multiplying each denominator

To demonstrate a scenario with denominators with common factors, let's say we need a common denominator for 24 and 36.  They both have 12 as a common factor.  12 "goes into" 24 twice (12*2=24) and 36 is 12*3.  So in this case the common denominator will be 12*2*3=72

Having said that, there is no harm in 24*36 as the common denomintor, but we use the above method for keeping the numbers small and making calculations easy

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