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22 Oct 2017, 10:07
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I was practicing some questions and one of them requires LCM of 66.66 and 50.
All the places I have seen gives LCM (66.66, 50) =200 but none of them have given steps of calculations so I am not able to find an easier solution to it.
My way is : Fraction LCM = \(\frac{LCM of numerator}{HFC of denominator}\)
\(\frac{6666}{100}\) and \(\frac{50}{1}\)= \(\frac{3333}{50}\) and \(\frac{50}{1}\)
So, \(\frac{LCM of 3333 and 50}{HCF of 50 and 1}\)
LCM :
3333 = 3 * 11* 101
50 = 5^2 * 2
This looks very complicated so I was wondering if I am doing it wrong or there is better way of doing it ?
All the places I have seen gives LCM (66.66, 50) =200 but none of them have given steps of calculations so I am not able to find an easier solution to it.
My way is : Fraction LCM = \(\frac{LCM of numerator}{HFC of denominator}\)
\(\frac{6666}{100}\) and \(\frac{50}{1}\)= \(\frac{3333}{50}\) and \(\frac{50}{1}\)
So, \(\frac{LCM of 3333 and 50}{HCF of 50 and 1}\)
LCM :
3333 = 3 * 11* 101
50 = 5^2 * 2
This looks very complicated so I was wondering if I am doing it wrong or there is better way of doing it ?
Archived Topic
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22 Oct 2017, 10:59
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you are correct that LCM of fractions = (LCM of numerators)/(HCF of denominators)
Now lets write the given numbers as fractions:
66.6666... (recurring) = 66 2/3 = 200/3
50 = 50/1
so LCM = (LCM of 50 & 200)/(HCF of 3 & 1) = 200/1 = 200
I think you are probably shortening the recurring decimal 66.6666... to 66.66 and hence this mismatch
Now lets write the given numbers as fractions:
66.6666... (recurring) = 66 2/3 = 200/3
50 = 50/1
so LCM = (LCM of 50 & 200)/(HCF of 3 & 1) = 200/1 = 200
I think you are probably shortening the recurring decimal 66.6666... to 66.66 and hence this mismatch
22 Oct 2017, 11:37
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amanvermagmat
Thanks! You made it look simple and I understood my mistake here. I was considering it to be non-recurring decimal places and the dividing the whole number by 100 to remove the decimal.
Now coming back to the actual question(below), how can I assume here that the decimal is recurring ? Did I miss a trick or assumption ?
"There are two bells in a temple. Both the bells toll at a regular interval of 66.66 sec and 50 sec respectively. After how much time will they toll together for the first time?"
