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Tag Archives: Number system tests for GRE preparation

Math Basics for GRE preparation - Part III

Number Properties, LCM and HCF

Plan of attack for some common problems

Important Results

S.No Type of Problem Approach
1 The GREATEST NUMBER that will exactly divide x, y, z. Required number = HCF of x, y, and z (greatest divisor)
2 The GREATEST NUMBER that will divide x, y, z leaving remainders a, b and c respectively Required number (greatest divisor) = HCF of (x-a), (y-b) and (z-c)
3. The LEAST NUMBER, which is exactly divisible by x, y and z Required number = LCM of x, y and z
4. The LEAST Number, which when divided by x, y and z leaves the remainders a, b, and c respectively. Then, it is always observed that (x-a) = (y-b) = (z-c) = M (say) therefore required number = (LCM of x, y and z)k – (K)
5 Find the LEAST Number, which when divided by x, y, and z leaves the same remainder ‘r’ in each case. Required number = (LCM of x, y and z) + r
6 Find the GREATEST NUMBER that will divide x, y and z leaving the same remainder in each case. Required number = HCF of (x-y), (y-z) and (z-x)

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