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Question

The greatest number, which when divided by 12, 15, 20 and 54 leaves a remainder of 8 in each case.
  1. 1620
  2. 1088
  3. 548
  4. Can’t determined


Solution

The correct option is D Can’t determined
We have to find the L.C.M of 12, 15, 20 and 54
The prime factor of 12=2×2×3=22×3
The prime factor of 15=3×5
The prime factor of 20=2×2×5=22×5
The prime factor of 54=2×3×3×3=2×33
L.C.M = Product of each prime factor with highest index used.
=22×33×5=540
The least number which give 8 as the remainder is 548 (540×1+8=548).
Similarly, second number which 8 as the remainder is 1088 (540×2+8=1088).
For third number, it is 1620 (540×3+8=1620).
So, we can’t able to find the largest number as we have infinite multiples of 540.
Hence, we can’t determine the greatest number, which when divided by 12, 15, 20 and 54 leaves a remainder of 8 in each case.

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