What will be the Least number? If

The least number which when divided by 48, 64, 90, 120 will leave remainders 38, 54, 80, 110 respectively, is

  1. 2870
  2. 2860
  3. 2890
  4. 2880
Monis Rasool Professor Asked on 8th June 2015 in Maths.
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1 Answer(s)

Answer:(3) 2890
Explanation:-
The LCM of 48 , 64, 90 and 120
48 = 2 x 2 x 2 x 2 x 3
64 = 2 x 2 x 2 x 2 x 2 x 2
90 = 2 x 3 x 3  x 5
120 = 2 x 2 x 2 x 3 x 5
LCM = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5
The LCM of 48, 64, 90 and 120 is 2880
Remainder –
48 – 38 = 10,       64 – 54 = 10,       90 – 80 = 10,       120 – 110 = 10
Thus, the least number is 2880 + 10 = 2890

Hence, the number is 2890.

Anurag Mishra Professor Answered on 9th June 2015.
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