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Find the smallest fraction, which if divided by 6/35 , 10/21, and 15/49 yields an integer.

Note by Ojasee Duble 1 year, 3 months ago

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2^{34}

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Let the fraction be \(\dfrac{x}{y}\),

To get integers when divided by \(\dfrac{6}{35},\dfrac{10}{21},\dfrac{15}{49}\),

\(x\) has to be the \(LCM(6,10,15)=30\) and,

\(y\) has to be the \(GCD (35,21,49)=7\)

\(\implies \dfrac{x}{y}=\dfrac{30}{7}\)

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Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewestLet the fraction be \(\dfrac{x}{y}\),

To get integers when divided by \(\dfrac{6}{35},\dfrac{10}{21},\dfrac{15}{49}\),

\(x\) has to be the \(LCM(6,10,15)=30\) and,

\(y\) has to be the \(GCD (35,21,49)=7\)

\(\implies \dfrac{x}{y}=\dfrac{30}{7}\)

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