Question

What is the least number which when divided by 18,27,36 leaves the remainders 5,14,23

Answer 1

Hi there!
Here's the answer:

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¶ Type of problem:

• To find the least number which when divided by x, y & z leaves remainder ' r ' in each case.

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¶ Approach to Problem:

- Then, it is always observed that:
( x - a) = ( y - b) = ( z - c) = k [ say ]

• Find L = LCM (x, y, z)

•°• Required No. = L - K

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¶¶ SOLUTION:

- Given
x = 18
y = 27
z = 36

a = 5
b = 14
c = 23

Here, k = 18-5 = 27-14 = 36-23 = 13

• Now, find LCM(18, 27, 36)

3 | 18, 27, 36
3 | 6, 9, 12
2 | 2, 3, 4
2 | 1, 3, 2

•°• L = 3×3×3×2×2×2
•°• L = 216


•°• Required No. = 216 - 13 = 203.

•°• The least number which when divided by 18,27,36 leaves the remainders 5,14,23 is 203.

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Verification:

• No. = 203

°•° Dividend = (Divisor × Quotient) + Remainder

203 = [ {18} × 11 ] + {5}
203 = [ {27} × 7 ] + {14}
203 = [ {36} × 5] + {23}

•°• Given Data matched

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Hope it helps