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How many integers between 1 and 200, inclusive, are divisible by both 3 and 4?

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by BTGmoderatorDC » Wed Aug 03, 2022 7:40 am

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How many integers between 1 and 200, inclusive, are divisible by both 3 and 4?

A. 8

B. 12

C. 15

D. 16

E. 24


OA D

Source: Princeton Review
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Re: How many integers between 1 and 200, inclusive, are divisible by both 3 and 4?

by swerve » Sun Aug 07, 2022 11:13 am
BTGmoderatorDC wrote: ↑
Wed Aug 03, 2022 7:40 am
 How many integers between 1 and 200, inclusive, are divisible by both 3 and 4?

A. 8

B. 12

C. 15

D. 16

E. 24


OA D

Source: Princeton Review
LCM of \(3\) and \(4\) is \(12\).

We need to look for multiples of \(12\) up to \(200\).

First multiple of \(12\) is \(12\)
Last multiple of \(12\) is \(192\)

Total integers \(= \dfrac{192 - 12}{12} + 1 = 15+1 = 16\).

Therefore, D
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