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A person has to completely put each of the threeliquids i.e. 403 litres of petrol, 465 litres of dieseland 496 litres of mobil oil in bottles of equal sizewithout mixing any of the three types of liquids suchthat each bottle is completely filled. What is the leastpossible number of bottles required ?

Question

A person has to completely put each of the threeliquids i.e. 403 litres of petrol, 465 litres of dieseland 496 litres of mobil oil in bottles of equal sizewithout mixing any of the three types of liquids suchthat each bottle is completely filled. What is the leastpossible number of bottles required ?

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Solution

To find the least possible number of bottles required, we need to determine the greatest common divisor (GCD) of the three given quantities: 403, 465, and 496.

Step 1: Find the GCD of 403 and 465.

  • Prime factorize 403: 403 = 13 * 31
  • Prime factorize 465: 465 = 3 * 5 * 31
  • The common prime factors are 31.
  • Therefore, the GCD of 403 and 465 is 31.

Step 2: Find the GCD of the result from Step 1 (31) and 496.

  • Prime factorize 496: 496 = 2^4 * 31
  • The common prime factor is 31.
  • Therefore, the GCD of 31 and 496 is 31.

Step 3: The least possible number of bottles required is equal to the GCD obtained in Step 2, which is 31.

Therefore, the least possible number of bottles required to completely put each of the three liquids in bottles of equal size without mixing any of the three types of liquids is 31.

This problem has been solved

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