Find the least number which when divided by 16 , 18 and 21 leaves the remainder 3 , 5 and 8 respectively.

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answer is A.

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Detailed Solution

Concept- In this case, take the numbers and their remainder terms out. Consequently, the necessary number will be equal to the least common multiple of the integers less than 13.
The numbers 16, 18, and 21 are provided. We are aware that the smallest number yields the following remainders when divided by 16, 18, and 21: 3, 5, and 8 accordingly. Let's now deduct 16 from its remainder to get 16-3=13.
Let's now subtracting 18 from its remainder to get,

Let's now remove number 21 from its remainder to obtain

Thus, the sum of the numbers after deduction with corresponding remainders is 13. Since,

Thus, the remainder of 3, 5, and 8 is always divided by 13, leaving 16, 18, and 21. The formula to get the least number is, We know that the least number is the one that when divided by 16, 18, and 21 leaves a residue of 3, 5, and 8,

Let's now determine what the least common factor between 16 and 18 and 21 is.
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Least common factor of 16,18 and 21

Least number=LCM(16,18,21)−13
Question Image

Hence, the correct answer is option 1.

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