Question

Three different containers contain different quantities of a mixture of milk and water whose measurements are \[403\,{\text{litres}}\] , \[434\,{\text{litres}}\] and \[465\,{\text{litres}}\] . What biggest measure must be there to measure all the different quantities exactly?
A. \[7\,{\text{litres}}\]
B. \[1\,{\text{litres}}\]
C. \[31\,{\text{litres}}\]
D. \[41\,{\text{litres}}\]

Answer 1

Hint: To find the biggest measure to measure all the different quantities exactly, you will need to find the highest common factor or H.C.F of the three given quantities. First write down the factors of each number and then check for the common factor among them to find the H.C.F

Complete step-by-step answer:
Given, three containers having the measurements \[403\,{\text{litres}}\] , \[434\,{\text{litres}}\] and \[465\,{\text{litres}}\] .

To find the biggest measure to measure all the different quantities we find the H.C.F of the numbers \[403\] , \[434\] and \[465\] .
H.C.F means highest common factor or the highest number that divides all the three numbers completely, that is with that value of measure we can measure all the three different quantities.
To find the H.C.F we check for the common factors of the three numbers \[403\] , \[434\] and \[465\] .
Factors of \[403\] , \[434\] and \[465\] are
 \[{\text{403}} = 31 \times 13\]
 \[434 = 2 \times 7 \times 31\]
 \[465 = 3 \times 5 \times 31\]
We observe that the common factor among the three numbers is \[31\] .
Therefore, the biggest measure to measure all the different quantities exactly is \[31\,{\text{litres}}\]
Hence, the correct answer is option (C) \[31\,{\text{litres}}\]
So, the correct answer is “Option C”.

Note: There are two terms H.C.F and L.C.M. Here we have discussed H.C.F and L.C.M means least common multiple that the smallest positive integer divisible by the given numbers. Also, remember that the product of L.C.M and H.C.F of any two given numbers is equal to the product of the numbers.