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Bunuel
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What is the lowest positive integer that is divisible by each of the 04 May 2021, 02:45
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C
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66% (01:37) correct 34% (01:18) wrong based on 112 sessions

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What is the lowest positive integer that is divisible by each of the odd integers between 15 and 21, inclusive?

(A) 3×17×19×21
(B) 5×17×19×23
(C) 7×15×17×19
(D) 7×15×19×21
(E) 15×17×19×21
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C
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What is the lowest positive integer that is divisible by each of the 08 May 2021, 00:30
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Bunuel
What is the lowest positive integer that is divisible by each of the odd integers between 15 and 21, inclusive?

(A) 3×17×19×21
(B) 5×17×19×23
(C) 7×15×17×19
(D) 7×15×19×21
(E) 15×17×19×21
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We should find the LCM of 15 = 3*5, 17, 19, and 21 = 3*7 --> LCM = 3*5*7*17*19 = 7*15*17*19.

Answer: C.
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prabha9899
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What is the lowest positive integer that is divisible by each of the 04 May 2021, 02:52
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IMO, The answer should be C.

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What is the lowest positive integer that is divisible by each of the 04 May 2021, 02:55
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Answer is C. 17*19*3*5*7 . All these are in C

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What is the lowest positive integer that is divisible by each of the 04 May 2021, 03:13
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Bunuel
What is the lowest positive integer that is divisible by each of the odd integers between 15 and 21, inclusive?

(A) 3×17×19×21
(B) 5×17×19×23
(C) 7×15×17×19
(D) 7×15×19×21
(E) 15×17×19×21
Show more

Asked: \(\frac{15×17×19×21}{x}\)
What is the smallest value of x? If we can maximize the quotient, we will have the smallest value of x.

1) \(\frac{15×17×19×21}{3×17×19×21}\) = 5

2) \(\frac{15×17×19×21}{5×17×19×23}\) = Not Divisible.

3) \(\frac{15×17×19×21}{7×15×17×19}\) = 3

4) \(\frac{15×17×19×21}{7×15×19×21}\) = Not Divisible.

5) \(\frac{15×17×19×21}{15×17×19×21}\) = 1

Option 1 has the biggest quotient of 5.
So, A) IMO :)
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What is the lowest positive integer that is divisible by each of the 06 May 2021, 01:36
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Bunuel
What is the lowest positive integer that is divisible by each of the odd integers between 15 and 21, inclusive?

(A) 3×17×19×21
(B) 5×17×19×23
(C) 7×15×17×19
(D) 7×15×19×21
(E) 15×17×19×21

Asked: \(\frac{15×17×19×21}{x}\)
What is the smallest value of x? If we can maximize the quotient, we will have the smallest value of x.

1) \(\frac{15×17×19×21}{3×17×19×21}\) = 5

2) \(\frac{15×17×19×21}{5×17×19×23}\) = Not Divisible.

3) \(\frac{15×17×19×21}{7×15×17×19}\) = 3

4) \(\frac{15×17×19×21}{7×15×19×21}\) = Not Divisible.

5) \(\frac{15×17×19×21}{15×17×19×21}\) = 1

Option 1 has the biggest quotient of 5.
So, A) IMO :)
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Here, we are asked what is the least number when divided by each of 15,17,19,21 will lead to a result which is basically asking us to find the LCM of (15,17,19,21).

So \(\frac{15×17×19×21}{x}\) is incorrect.

The question stem means we have to find a number which when divided by each of odd numbers from 15 to 21 wont give any remainder besides 0.


Calculating the LCM of these 4 numbers will lead you to Option C.
On calculation you will also find that the numerator is completely divisible by the denominator.
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What is the lowest positive integer that is divisible by each of the 08 May 2021, 00:52
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What is the lowest positive integer that is divisible by each of the odd integers between 15 and 21, inclusive?

15= 3*5 and 21 = 3*7

So, C is the lowest value having, 3,5 and 7 factors.
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What is the lowest positive integer that is divisible by each of the 22 Nov 2023, 11:24
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