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The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:
- a)534
- b)486
- c)544
- d)548
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The least number, which when divided by 12, 15, 20 and 54 leaves in ea...
Required number = (L.C.M. of 12, 15, 20, 54) + 8
= 540 + 8
= 548.
= 540 + 8
= 548.
Most Upvoted Answer
The least number, which when divided by 12, 15, 20 and 54 leaves in ea...
To find the least number that leaves a remainder of 8 when divided by 12, 15, 20, and 54, we need to find the least common multiple (LCM) of these numbers.
Finding LCM:
First, we list the multiples of each number until we find a common multiple.
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, ...
Multiples of 20: 20, 40, 60, 80, 100, 120, ...
Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, ...
From the lists above, we can see that the common multiple is 120.
Adding the remainder:
Now, we need to find the number that leaves a remainder of 8 when divided by 120. We can do this by adding the remainder to the LCM.
120 + 8 = 128
Therefore, the least number that satisfies the given condition is 128.
However, none of the answer options provided in the question match 128. Let's check the options:
a) 534: Not divisible by 12, 15, 20, or 54
b) 486: Not divisible by 12, 15, 20, or 54
c) 544: Not divisible by 12, 15, 20, or 54
d) 548: Not divisible by 12, 15, 20, or 54
e) None of these
Since none of the options match the correct answer, it seems that there might be an error in the given question or answer choices.
Finding LCM:
First, we list the multiples of each number until we find a common multiple.
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, ...
Multiples of 20: 20, 40, 60, 80, 100, 120, ...
Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, ...
From the lists above, we can see that the common multiple is 120.
Adding the remainder:
Now, we need to find the number that leaves a remainder of 8 when divided by 120. We can do this by adding the remainder to the LCM.
120 + 8 = 128
Therefore, the least number that satisfies the given condition is 128.
However, none of the answer options provided in the question match 128. Let's check the options:
a) 534: Not divisible by 12, 15, 20, or 54
b) 486: Not divisible by 12, 15, 20, or 54
c) 544: Not divisible by 12, 15, 20, or 54
d) 548: Not divisible by 12, 15, 20, or 54
e) None of these
Since none of the options match the correct answer, it seems that there might be an error in the given question or answer choices.
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