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Q.

Find the least number which is a multiple of 23, and on division by 18, 21 and 24 leaves the remainder 7, 10 and 13 respectively.

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a

3301

b

3103

c

3013

d

3130

answer is C.

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Detailed Solution

Concept: First, we will take LCM of the given numbers and then use the formula

where R is

and M, n are variables.
After that, we will use the hit and trial method by substituting the values of M and then check whether the number is divided by 23 or not.
LCM of numbers 18, 21 and 24 is 504.
Let us assume that the number is 504k.
According to the question:
Question Image

Question Image

Now we will put the value of k such that it should be divisible by 23.
Question Image

Question Image

Hence, the correct answer is option (3).

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