What is the smallest integer greater than 200 for which the greatest common divisor of that integer and 36 is 18?

Mellie
Jun 23, 2015

#1**+10 **

Seing as the only greater divisor of 36 is...36, then all we need to care about is avoiding it being divisble by 36 but keeping it divisible by 18.

Simply just make sure it has an **odd** number of 18s in it.

So 18 * x > 200 where x ∈ odd

See how close we are with just 200.

200 / 18 = 11.1 [*1 recurring]*

Okay well this is the bottom limit of what we can use for x.

The next integer along that we can use is 12, but that's an even number, so let's go to 13 instead.

This will be the first instance where 18 * x > 200, and x is not even.

18 * 13 = **234**

**To check:**

234 / 18 = 13

234 / 36 = 6.5

18 is a factor, but 36 is not.

Sir-Emo-Chappington
Jun 23, 2015

#1**+10 **

Best Answer

Seing as the only greater divisor of 36 is...36, then all we need to care about is avoiding it being divisble by 36 but keeping it divisible by 18.

Simply just make sure it has an **odd** number of 18s in it.

So 18 * x > 200 where x ∈ odd

See how close we are with just 200.

200 / 18 = 11.1 [*1 recurring]*

Okay well this is the bottom limit of what we can use for x.

The next integer along that we can use is 12, but that's an even number, so let's go to 13 instead.

This will be the first instance where 18 * x > 200, and x is not even.

18 * 13 = **234**

**To check:**

234 / 18 = 13

234 / 36 = 6.5

18 is a factor, but 36 is not.

Sir-Emo-Chappington
Jun 23, 2015