Aptitude - Problems on H.C.F and L.C.M - Discussion

48, 92 and 140 = 4 how now am confusing, please explain.

@ Sanddep:

Have a look at explanation given by @Prasant. We have to solve equation for 'p'. Hence,we eliminate 'r' by taking differences of numbers.

I don't understand why you write 2*2 and say the answer is 4.

Why we take HCF? When one should take LCM and HCF.

Why did we take the differences of the numbers?

Is this the only way to solve it by taking the differences if there is any other method then please reply?

Here 4 is even number. So its multiples will also be even. In the question above all the numbers were odd. If is divide by 4 then it will compulsory leaves an remainder.

Divided by 4 each number we get remainder 3

Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

Explanation: 43, 91, 183.
183 = (183-91) = 92.
91 = (183-43) = 140.
43 = (91-43) = 48.

92, 140, 48.

92 = 2*2*23.
140 = 2*2*35.
48 = 2*2*2*3*2.

Ans 4.

As it is asking for greatest no among all options the answer for above problem should be 7 as it divides all the no and gives remainder 0.

1.The HCF of two or more numbers is the largest common factor of the given numbers. It is the smallest number which divides the two or more given numbers.

The LCM of two or more numbers is the smallest number that is a common multiple of two or more numbers. It is the smallest number which is divisible by two or more given numbers.

Consider two numbers 120 and 144.
Prime factorization of 120 = 2 x 2 x 2 x 3 x 5
Prime factorization of 144 = 2 x 2 x 2 x 2 x 3 x 3
HCF of 120 and 144 = 2 x 2 x 2 x 3 = 24. 24 is the smallest number which divides both 120 and 144.

LCM of 120 and 144 = 2 x 2 x 2 x 2 x 3 x 3 x 5 = 720. 720 is the smallest number which is divisible by both 120 and 144. NOTE IT IS THE INTERSECTION OF THE PRIME FACTORS WHEN MULTIPLIED THAT GIVES THE HCF. AND AUNIVERSAL THAT GIVES THE LCM.

HIGHEST COMMON FACTOR (H.C.F).
LOWEST COMMON MULTIPLE (L.C.M.).