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What is the least possible number which when divided by 24, 32 or 42 in each case it leaves the remainder 5.how many numbers are possible between 666 and 8888?
- a)10
- b)11
- c)12
- d)13
Correct answer is 'D'. Can you explain this answer?
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Most Upvoted Answer
What is the least possible number which when divided by 24, 32 or 42 i...
The least common factor of 24, 32 and 42 is 672. Now the least number which leaves a reminder of 5 when divided with all the above three numbers is,
672 + 5 = 677
Starting from 677 to get all such numbers we must add 672 to the preceding number. To say all these numbers will be in AP whose first term is 677 and common difference is 672. For finding number of terms in the series which are less than 8888 find what in position will be the number 8888.
8888 = 677 + 672(n - 1)
n = 1 + (8888 - 677)/672 = 13.21
Therefore there will be 13 such numbers less than 8888
672 + 5 = 677
Starting from 677 to get all such numbers we must add 672 to the preceding number. To say all these numbers will be in AP whose first term is 677 and common difference is 672. For finding number of terms in the series which are less than 8888 find what in position will be the number 8888.
8888 = 677 + 672(n - 1)
n = 1 + (8888 - 677)/672 = 13.21
Therefore there will be 13 such numbers less than 8888
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What is the least possible number which when divided by 24, 32 or 42 i...
Finding the Least Possible Number
To find the least possible number, we need to find the LCM of 24, 32, and 42 and add 5 to it. The LCM of these numbers is 672, so the least possible number is 672 + 5 = 677.
Finding the Number of Possible Numbers between 666 and 8888
To find the number of possible numbers between 666 and 8888 that leave a remainder of 5 when divided by 24, 32, or 42, we need to find the multiples of 24, 32, and 42 that are greater than or equal to 666 and less than or equal to 8888, and then count the numbers that leave a remainder of 5.
Multiples of 24 between 666 and 8888:
The smallest multiple of 24 that is greater than or equal to 666 is 672.
The largest multiple of 24 that is less than or equal to 8888 is 8880.
To find the number of multiples of 24 that leave a remainder of 5, we need to find the multiples of 24 that are congruent to 5 modulo 24.
The first multiple of 24 that is congruent to 5 modulo 24 is 29.
The next multiple of 24 that is congruent to 5 modulo 24 is 53.
The last multiple of 24 that is less than or equal to 8880 and congruent to 5 modulo 24 is 8869.
Therefore, there are 370 multiples of 24 between 666 and 8888 that leave a remainder of 5 when divided by 24.
Multiples of 32 between 666 and 8888:
The smallest multiple of 32 that is greater than or equal to 666 is 672.
The largest multiple of 32 that is less than or equal to 8888 is 8864.
To find the number of multiples of 32 that leave a remainder of 5, we need to find the multiples of 32 that are congruent to 5 modulo 32.
The first multiple of 32 that is congruent to 5 modulo 32 is 37.
The next multiple of 32 that is congruent to 5 modulo 32 is 69.
The last multiple of 32 that is less than or equal to 8864 and congruent to 5 modulo 32 is 8837.
Therefore, there are 276 multiples of 32 between 666 and 8888 that leave a remainder of 5 when divided by 32.
Multiples of 42 between 666 and 8888:
The smallest multiple of 42 that is greater than or equal to 666 is 672.
The largest multiple of 42 that is less than or equal to 8888 is 8886.
To find the number of multiples of 42 that leave a remainder of 5, we need to find the multiples of 42 that are congruent to 5 modulo 42.
The first multiple of 42 that is congruent to 5 modulo 42 is 47.
The next multiple of 42 that is congruent to 5 modulo 42 is 89.
The last multiple of 42 that is less than or equal to 8886 and congruent to 5 modulo 42 is 8833.
Therefore,
To find the least possible number, we need to find the LCM of 24, 32, and 42 and add 5 to it. The LCM of these numbers is 672, so the least possible number is 672 + 5 = 677.
Finding the Number of Possible Numbers between 666 and 8888
To find the number of possible numbers between 666 and 8888 that leave a remainder of 5 when divided by 24, 32, or 42, we need to find the multiples of 24, 32, and 42 that are greater than or equal to 666 and less than or equal to 8888, and then count the numbers that leave a remainder of 5.
Multiples of 24 between 666 and 8888:
The smallest multiple of 24 that is greater than or equal to 666 is 672.
The largest multiple of 24 that is less than or equal to 8888 is 8880.
To find the number of multiples of 24 that leave a remainder of 5, we need to find the multiples of 24 that are congruent to 5 modulo 24.
The first multiple of 24 that is congruent to 5 modulo 24 is 29.
The next multiple of 24 that is congruent to 5 modulo 24 is 53.
The last multiple of 24 that is less than or equal to 8880 and congruent to 5 modulo 24 is 8869.
Therefore, there are 370 multiples of 24 between 666 and 8888 that leave a remainder of 5 when divided by 24.
Multiples of 32 between 666 and 8888:
The smallest multiple of 32 that is greater than or equal to 666 is 672.
The largest multiple of 32 that is less than or equal to 8888 is 8864.
To find the number of multiples of 32 that leave a remainder of 5, we need to find the multiples of 32 that are congruent to 5 modulo 32.
The first multiple of 32 that is congruent to 5 modulo 32 is 37.
The next multiple of 32 that is congruent to 5 modulo 32 is 69.
The last multiple of 32 that is less than or equal to 8864 and congruent to 5 modulo 32 is 8837.
Therefore, there are 276 multiples of 32 between 666 and 8888 that leave a remainder of 5 when divided by 32.
Multiples of 42 between 666 and 8888:
The smallest multiple of 42 that is greater than or equal to 666 is 672.
The largest multiple of 42 that is less than or equal to 8888 is 8886.
To find the number of multiples of 42 that leave a remainder of 5, we need to find the multiples of 42 that are congruent to 5 modulo 42.
The first multiple of 42 that is congruent to 5 modulo 42 is 47.
The next multiple of 42 that is congruent to 5 modulo 42 is 89.
The last multiple of 42 that is less than or equal to 8886 and congruent to 5 modulo 42 is 8833.
Therefore,
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