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Re: What is the lowest positive integer that is divisible by [#permalink]
11 Sep 2012, 08:24
1
This post received KUDOS
Factors of 420 are: 1, 2, 2, 3, 5, 7
Now 420 should be divided by each of 1, 2, 3, 4, 5, 6, 7
From the factors which we get above by factorization and combining them to make all numbers from 1 to 7,
420 divided by 1 420 divided by 2 (picking up from factors) 420 divided by 3 (picking up from factors) 420 divided by 4 (picking up two 2s and multiplying to make it 4) 420 divided by 5 (picking up from factors) 420 divided by 6 (picking up 2 and 3 from factors and multiplying to make it 6) 420 divided by 7 (picking up from factors) All leaves remainder as ZERO.
No need to go further. Answer is A. _________________
Re: What is the lowest positive integer that is divisible by [#permalink]
11 Sep 2012, 09:07
1
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Here are the integers from 1 to 7 including: 1, 2, 3, 4, 5, 6, 7 So the lowest positive integer divisible by every single numbers set forth above would have to be divisible by 7,5,4,3 simultaneously or 7*5*4*3=420 please, correct me if I went awry _________________
What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive? (A) 420 (B) 840 (C) 1,260 (D) 2,520 (E) 5,040
My choice is E.But its wrong. My Explanation:lowest positive integer that is divisible by each of the integers 1 through 7 means 7!. 7!=5040.Hence (E) However this answer is wrong. I am not able to understand the OG12 explanation
Re: What is the lowest positive integer that is divisible by [#permalink]
13 Jan 2013, 22:43
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You need LCM of first 7 numbers, NOT factorial. If a number is divisible by 6 then its also divisible by 2 & 3. You dont have to count 2 & 3 again when you consider factor as 6.
What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive? (A) 420 (B) 840 (C) 1,260 (D) 2,520 (E) 5,040
My choice is E.But its wrong. My Explanation:lowest positive integer that is divisible by each of the integers 1 through 7 means 7!. 7!=5040.Hence (E) However this answer is wrong. I am not able to understand the OG12 explanation
Merging similar topics. Please ask if anything remains unclear.
P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3: the name of a topic (subject field) MUST be the first 40 characters (~the first two sentences) of the question. _________________
Re: What is the lowest positive integer that is divisible by [#permalink]
17 Jan 2013, 02:58
PraPon wrote:
You need LCM of first 7 numbers, NOT factorial. If a number is divisible by 6 then its also divisible by 2 & 3. You dont have to count 2 & 3 again when you consider factor as 6.
Re: What is the lowest positive integer that is divisible by [#permalink]
17 Jan 2013, 08:31
the question stem says that the number is divisible by each of the integers from 1 through 7..then,simply,it means that each number is a factor of our lowest common multiple..hence 420 holds water
Re: What is the lowest positive integer that is divisible by [#permalink]
29 Dec 2013, 10:01
Bunuel wrote:
SOLUTION
What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?
(A) 420 (B) 840 (C) 1,260 (D) 2,520 (E) 5,040
The integer should be divisible by: 2, 3, 4(=2^2), 5, 6(=2*3), and 7. The least common multiple of these integers is LCM=2^2*3*5*7=420.
Answer: A.
Hi Bunuel,
I do understand the LCM but can you explain WHY when we have four sets of 2's we eliminate TWO of them?
For our two 3's, we eliminate one of them and I understand why - we might have the "same" 3. But when we eliminate two 2's, it's not as intuitive to me. Is it simply that, when we have an even number of the same integer, we remove half of them when we calculate the LCM? If so, what would've happened if we had three 2's or five 3's?
Re: What is the lowest positive integer that is divisible by [#permalink]
29 Dec 2013, 10:20
Expert's post
aeglorre wrote:
Bunuel wrote:
SOLUTION
What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?
(A) 420 (B) 840 (C) 1,260 (D) 2,520 (E) 5,040
The integer should be divisible by: 2, 3, 4(=2^2), 5, 6(=2*3), and 7. The least common multiple of these integers is LCM=2^2*3*5*7=420.
Answer: A.
Hi Bunuel,
I do understand the LCM but can you explain WHY when we have four sets of 2's we eliminate TWO of them?
For our two 3's, we eliminate one of them and I understand why - we might have the "same" 3. But when we eliminate two 2's, it's not as intuitive to me. Is it simply that, when we have an even number of the same integer, we remove half of them when we calculate the LCM? If so, what would've happened if we had three 2's or five 3's?
The lowest common multiple or lowest common multiple (lcm) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple both of a and of b.
To find the LCM, you will need to do prime-factorization. Then multiply all the factors (pick the highest power of the common factors). _________________
What is the lowest positive integer that is divisible by [#permalink]
24 Nov 2014, 12:46
Bunuel wrote:
What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?
(A) 420 (B) 840 (C) 1,260 (D) 2,520 (E) 5,040
Practice Questions Question: 40 Page: 157 Difficulty: 600
With this approach, if LCM of these numbers(from 1 to 7) was not available in options, than precious time could have been wasted while calculating LCM.
So in my opinion the quickest and most accurate approach would be to check the divisibility of each given option (by starting with lowest one) by using following rules:
3>>>>sum of digits should be divisible by 3 6>>>>integer should be divisible by both 2 and 3 9>>>>sum of digits should be divisible by 9 4>>>>should be divisible by 2 twice 5>>>>should be 0 or 5 in the end 7>>>>check divisibility in normal way
What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?
A) 420 B) 840 C) 1260 D) 2520 E) 5040
Seeking a better explanation for the answer and a faster way to solve. In my approach I attempted to figure out if each term was divisible by each 1, 2, 3, 4, 5, 6, and 7, starting with D and B. I see now this was not the right approach. In reviewing the explanation provided from MGMAT, I am still confused and would appreciate clarification on how to solve.
What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?
A) 420 B) 840 C) 1260 D) 2520 E) 5040
Seeking a better explanation for the answer and a faster way to solve. In my approach I attempted to figure out if each term was divisible by each 1, 2, 3, 4, 5, 6, and 7, starting with D and B. I see now this was not the right approach. In reviewing the explanation provided from MGMAT, I am still confused and would appreciate clarification on how to solve.
Search for a question before posting. Topics merged.
For LCM of 2 numbers, you need to break down the numbers to their prime factors and then the LCM will be composed of the product of prime factors raised to the heighest power in either of the 2 numbers.
In the given question, you had 2 as the highest power of 2 and 1 as the highest power of 3,5,7 _________________
What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?
A) 420 B) 840 C) 1260 D) 2520 E) 5040
Seeking a better explanation for the answer and a faster way to solve. In my approach I attempted to figure out if each term was divisible by each 1, 2, 3, 4, 5, 6, and 7, starting with D and B. I see now this was not the right approach. In reviewing the explanation provided from MGMAT, I am still confused and would appreciate clarification on how to solve.
We simply need to find the LCM of 1,2,3,4,5,6,7 here and that is 420.
LCM of a set of numbers is the product of highest powers of primes numbers in that set. In this case LCM = 1*2^2*3*5*7 = 420
Moreover, if you are testing options in a question that asks you to find the lowest value, you should always start with the lowest one. This ways if the answer is the lowest option (as is the case here), yo do not need to look further. _________________
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