1.Find the greatest number of 4 digits which when divided by 12,18,and 24 leaves a remainder 6 in each case.
2.Find the least number of five digits which on dividing by 15,20,25,30, and 35 leaves a remainder 7 in each case.
3.Find the smallest 4 digit number which is exactly divisible by 6,8, and 12.
4.Find the largest 4 digit number which when divided by 16,24 and 32.
i)leaves no remainder.
ii)leaves a remainder 8 in all case.

Asked by malini11desai | 16th Sep, 2016, 09:31: AM

Expert Answer:

begin mathsize 12px style left parenthesis 1 right parenthesis space The space greatest space 4 space digit space number space is space 9999. First space find space the space LCM space of space 12 comma space 18 space and space 24. LCM space of space 12 comma space 18 space and space 24 space is space 72. Now comma space 9999 over 72 equals 138 comma space Remainder space will space be space 63 rightwards double arrow The space required space number space equals space left parenthesis 9999 minus 63 right parenthesis plus 6 equals 9942 left parenthesis 2 right parenthesis space The space smallest space five space digit space number space is space 10000. The space LCM thin space of space 15 comma space 20 comma space 25 comma space 30 space and space 35 space is space 2100 Now comma space 10000 over 2100 equals 4 comma space Remainder space will space be space 1600 rightwards double arrow The space required space number equals 10000 plus left parenthesis 2100 minus 1600 right parenthesis plus 7 equals 10507 left parenthesis 3 right parenthesis space The space smallest space four space digit space number space is space 1000. The space LCM space of space 6 comma space 8 space and space 12 space is space 24. Now comma space 1000 over 24 equals 41 comma space Remainder space equals space 16 rightwards double arrow The space required space number equals 1000 plus 24 minus 16 equals 1008 left parenthesis 4 right parenthesis space The space largest space 4 space digit space number space is space 9999. LCM space of space 16 comma space 24 space and space 32 space is space 96 Now comma space 9999 over 96 equals 104 comma space Remainder space equals 15 left parenthesis straight i right parenthesis space If space the space number space leaves space no space remainder comma space the space required space number equals 9999 minus 15 equals 9984 left parenthesis ii right parenthesis space If space the space number space leaves space straight a space remainder space 8 space in space all space cases comma space the space required space number equals 9999 minus 15 plus 8 equals 9992 Kindly space post space one space query space at space straight a space time. end style

Answered by Rebecca Fernandes | 16th Sep, 2016, 10:03: PM

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