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

The smallest number divisible by 12,32,42 and 63 is its LCM which is 2016.

The prime factorization of 2016 is 2x2x2x2x2x3x3x7.

Pick out the pairs in this step. They are 2x2 2x2 3x3.

2 and 7 are not in pairs. But if there is one more 2 and one more 7, both 2 and 7 can also be in pairs.

So the required numbers are one more 2 and one more 7. So it is 2x7= 14. Therefore, 2016x14 = 28224.

So the required square number is 28224.

Thank you!

HCF of two numbers is 12, their sum is 72, then the two numbers are?

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.).

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.

Divided by 4 each number we get remainder 3

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.

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?

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

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

@ 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.