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30 Mar 2013, 03:03
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Is there an algebraic way to calculate the least common denominator (LCM) of several numbers?
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30 Mar 2013, 03:51
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Suppose you are calculating the least common denominator of fractions with denominators 4 and 12 then you can use the following method
2 | 4, 12
2 | 2, 6
| 1, 3
so least common denominator will be 2*2*1*3 = 12
Here, we first divided 4 and 12 by their common divisor , which is 2 and we wrote the quotient in the second row which gave us 2 and 6
then we divided 2 and 6 by their common divisor , which is 2 and we wrote the quotient in the second row which gave us 1 and 3
now 1 and 3 do not a factor other than 1 so we multiply 2 , 2, 1 and 3 to get the least common divisor which is 12
Above thing could have been done in one more way
4 | 4,12
| 1,3
LCM = 4*1*3 = 12
This is a common approach to find LCM. (and thus Least Common Denominator)
This method can also be used to find HCF
4 | 4,12
| 1,3
HCF will be 4... it is nothing but the highest common multiple of both the numbers in consideration.
The same approach can be used to 3,4 or any number of numbers
LCM of 4,8,12
4 | 4,8,12
| 1,2,3
LCM = 4*1*2*3 = 24
Hope it helps!
Watch the following video to Learn the Basics of LCM and GCD
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