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

23 is common in both.

13 and 14 are factors of lcm thus may be common or may occur separate in both number but if they were commen then they should be included into hcf and that is not so.

Therefore 13 and 14 comes separately in both number.

Thus 23*13 and 23*14.

See definitions of H. C. F and L. C. M.
HCF=the product of common factor with least index.
LCM=product of all the prime factor of each of the given num with greatest index.
A/c to given question.
23 is the HCF of TWO given num.
And other two factor 13, 14 of the LCM.
Note :-here 14 is not a prime num hence 14=2*7.
It is clear that 23 is that prime num which is come in the LCM of two number.
Hence total prime number is (2, 7, 13, and 23).
Hence one num is 13*23=299.
And 2nd is=2*7*23.
Answer is (2*7*23).

With this concepts children will not be able to understand as they have been taught in school the other way.

The best solution is,

Since the factors of the lcm of 2 nos are 13, 14 then lcm of the 2 nos will be (13x14) = 182.

This means the lcm of the 2 nos is 182 answer as said that the hcf of the 2 nos is 23.

We know that LCM x HCF = product of the 2 nos.

So 182 x 23 = the product.

So product = 4186.

As factors are 13 and 14.

The nos are 4186/13 = 322 and 4186/14 = 299.

So the bigger of the 2 is 322.

Product of l.c.m and h.cf is that numbers so in the same way hcf is 23 and l.cm 13 and 4 are given and ther the ans 23*14 is right

@Neha you are right. , how can we multiply 23 twice, I think Darknight's explanation is good. ,

@Chiya a*(b*c) is not equal to (a*b)*(b*c).... :D

@Chiya explains good.

Let &b r 2 nos.
NOW HCF*LCM=a*b
13 &14 are two factors of lcm ok
now lcm=a*13 (by defination of lcm && in the question it is given that there r 2 factors)
sim. lcm=b*14
23*lcm=a*b
23*a*13=a*b
so clearly b=23*13
a=23*13
solved!!!!

Why l.c.m is a multiple of uncommon factors? if we take l.c.m of 2,4,6 then its l.c.m is 2*2*3=12 but when we multiply the uncommon factors i.e 2*3=6.

If the two Nos are A and B.

LCM factor of A=13 and that of B=14 (by doing LCM).

And HCF of A and B is 23.

Than the No is always HCF*A =23*13 / HCF*B=23 *14.

Hence B=322 is larger No.