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Welcome to your H.C.F. AND L.C.M.

The greatest number, which when subtracted from 5834, gives a number exactly divisible by each of 20, 28, 32 and 35 is [SSC CGL 2010]
Find the least multiple of 23, which when divided by 18, 21 and 24 leaves the remainder 7, 10 and 13 respectively.
The greatest number of four digits which when divided by 3, 5, 7, 9 leave remainders 1, 3, 5, 7 respectively is [SSC 2012]
The largest number of five digits which, when divided by 16, 24, 30 or 36 leaves the same remainder 10 in each case is
A farmer has 945 cows and 2475 sheep. He farms them into flocks, keeping the cows and sheep separately and having the same number of animals in each flock. If these flocks are as large as possible, then the maximum number of animals in each flock and the total number of flocks required for the purpose are respectively [SSC 2011]
A number between 1000 and 2000 which when divided by 30, 36 and 80 gives a remainder 11 in each case is [SSC 2015]
Let N be the greatest number that will divide 1305, 4665 and 6905 leaving the same remainder in each case. Then, the sum of the digits in N is
If the H.C.F. and L.C.M. of two consecutive (positive) even numbers be 2 and 84 respectively, then the sum of the numbers is [SSC 2011]
A fraction becomes (1/6) when 4 is subtracted from its numerator and 1 is added to its denominator. If 2 and 1 are respectively added to its numerator and the denominator, it becomes (1/3). Then, the L.C.M. of the numerator and denominator of the said fraction, must be [SSC CGL 2011]

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