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# The number of students who attend a school could be divided among 10,

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Re: The number of students who attend a school could be divided among 10, [#permalink]
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Bunuel wrote:
The number of students who attend a school could be divided among 10, 12, or 16 buses, such that each bus transports an equal number of students. What is the minimum number of students that could attend the school?

(A) 120
(B) 160
(C) 240
(D) 320
(E) 480

The number of students who attend a school could be divided among 10, 12, or 16 buses, such that each bus transports an equal number of students.
This tells us that the TOTAL number of students is a multiple of 10, 12 and 16

What is the minimum number of students that could attend the school?
This whole question is a clever way to ask "What is the LEAST common multiple of 10, 12, and 16?"

Since the answer choices are written is ASCENDING order, we can just start with answer choice A and keep checking answers until we find a value that is a multiple of 10, 12, and 16

(A) 120. This is NOT divisible by 16. ELIMINATE
(B) 160. This is NOT divisible by 12. ELIMINATE
(C) 240. This is divisible by 10, 12, and 16

Cheers,
Brent
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Re: The number of students who attend a school could be divided among 10, [#permalink]
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This is a prime factorisation question.
https://www.mathsisfun.com/prime-factorization.html

$$10=5^1·2^1$$
$$12=2^2·3^1$$
$$16=2^4$$

So the lowest common multiple is $$2^4·3^1·5^1=$$
(C) 240
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Re: The number of students who attend a school could be divided among 10, [#permalink]
Bunuel wrote:
The number of students who attend a school could be divided among 10, 12, or 16 buses, such that each bus transports an equal number of students. What is the minimum number of students that could attend the school?

(A) 120
(B) 160
(C) 240
(D) 320
(E) 480

LCM of 10, 12, or 16 buses, will give you the minimum number of students that could attend the school

C
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Re: The number of students who attend a school could be divided among 10, [#permalink]
Hi there,

There is no direct importance of LCM.

We have to understand question language and solve it by that language.
Suppsue we have X number of equal students, who come by Bus to attend school.

So here, 10X, 12X, and 16X students can attend school.

Now, X is common in all types of Buses and students multiple. We have to find minimum means least. So basically we have to find the least common multiple / LCM.

Then we can talk about LCM. The LCM of these factors is 240.

Thanks and Regards
Jatin Anand
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Re: The number of students who attend a school could be divided among 10, [#permalink]
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Re: The number of students who attend a school could be divided among 10, [#permalink]
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