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

Why we have to take difference of two number?

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.

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

What is different between HCF & LCM?
And what is the meaning HCF & LCM?

Why we have to take the difference of the numbers can you please explain?

Why we have to take the difference of the numbers please explain?

@ Merry.

Pratibhan meant, the common thing coming in prime factor list of all 3 nos is 2*2, i.e 4.

When pratibhan said the common factor is 2 ok this is write but why she multiple two no of 2 whyn't three no of 2 means the result is 8.

If three nos as in this case is 43, 91 and 183 are given then to find HCF the shortest solution is take the diff:

1) 91 - 43 = 48 (4*3*7).
2) 183 - 91 = 92 (4*23).
3) 183 - 43 = 140 (4*7*5).

Thus the HCF is 4.

@Cathy.

The keyword is greatest or largest- if you find these words, we are required to find HCF. If in case you find least or lowest in the problem, we need to find LCM.

How do you know we are to find the h.C.F ?

I seem to be getting so confused.