Find the least positive integer which on being diminished by 5 is exactly divisible by 36 and 54.

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120

113

100

243

answer is B.

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Detailed Solution

Given,
The numbers are 36 and 54.
Let the least positive integer is x ,
According to question , if 5 is subtracted from it then it is completely divisible by 36 and 54, that is,

⇒ x − 5 = L C M (36, 54)

As the least positive integer is equal to the LCM of 36 and 54,
Prime factors of numbers are,

⇒ 36 = 2 × 2 × 3 × 3 ⇒ 36 = 22 × 32

⇒ 54 = 2 × 3 × 3 × 3 ⇒ 54 = 2 × 33

⇒ L C M 36, 54 = 22 × 33

⇒ L C M 36, 54 = 4 × 27

⇒ L C M 36, 54 = 108

Now, as per the question,

⇒ L C M 36, 54 = x − 5

⇒ 108 = x − 5

⇒ x = 113

Thus, the least positive integer is 113.
Therefore, option(2) is correct answer.

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