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Let x be the least four-digit number which when divided by 18, 27, 30, 40 and 45, the remainder in each case is 9. Find the remainder when x is divided by 37.

Let x be the least four-digit number which when divided by 18, 27, 30, 40 and 45, the remainder in each case is 9. Find the remainder when x is divided by 37. Correct Answer 16

Given:

x be the least four-digit number which when divided by 18, 27, 30, 40 and 45, the remainder in each case is 9.

Concept used:

LCM of two or more numbers is the smallest common multiple of two or more numbers.

Dividend = Divisor × Quotient + Remainder

Calculation:

The smallest number that is when divided by 18, 27, 30, 40, and 45 leaves a remainder of 0 in each case is the LCM of these numbers. 

LCM (18, 27, 30, 40, 45) = 1080

Now, x is the smallest number that is when divided by 18, 27, 30, 40, and 45, leaves a remainder of 9 in each case.

Hence, x = 1080 + 9 = 1089

Now,

1089

⇒ 37 × 29 + 16

∴ When x is divided by 37, it leaves a remainder of 16.

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