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# LCM of 66.66 and 50 or 33.33 and 25

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Intern
Joined: 25 Sep 2017
Posts: 3
LCM of 66.66 and 50 or 33.33 and 25 [#permalink]

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22 Oct 2017, 10:07
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 ?
DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1209
Location: India
Re: LCM of 66.66 and 50 or 33.33 and 25 [#permalink]

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22 Oct 2017, 10:59
1
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
Intern
Joined: 25 Sep 2017
Posts: 3
LCM of 66.66 and 50 or 33.33 and 25 [#permalink]

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22 Oct 2017, 11:37
amanvermagmat wrote:
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

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?"
DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1209
Location: India
Re: LCM of 66.66 and 50 or 33.33 and 25 [#permalink]

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22 Oct 2017, 22:04
ramanbajwa2003 wrote:
amanvermagmat wrote:
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

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?"

Well the question doesn't state that its recurring, it just writes 66.66. But in such cases its mostly better to assume recurring because then we can easily convert them to decimal. I suggest if answer options are in integers then you assume the decimal to be recurring only.

But yes ideally the question should have specified that it was a recurring decimal.
Re: LCM of 66.66 and 50 or 33.33 and 25   [#permalink] 22 Oct 2017, 22:04
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