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

Discussion Forum : Problems on H.C.F and L.C.M - General Questions (Q.No. 2)
2.
The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
276
299
322
345
Answer: Option
Explanation:

Clearly, the numbers are (23 x 13) and (23 x 14).

Larger number = (23 x 14) = 322.

Discussion:
153 comments Page 7 of 16.

Gaurav said:   8 years ago
Let first no. = 23a.
Second no. = 23b.
So lcm = 23 ab.
Now give attention to the question, that it is saying other to factors of lcm are 13 and 14 so it means there are only three factors in lcm which are 23,13 and 14 so I think that's why a=13 and b = 14.

Darknight said:   1 decade ago
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!!!!

Cibi said:   1 decade ago
L.C.M of two Numbers x1 = 13 & x2 = 14.
H.C.F (highest common factor) of x1 & x2 is = 23.

Therefore x1 = 23 & x2 = 23.

Largest Number is,

L.C.M(x1)*H.C.F(x1) = 13*23 = 299.
L.C.M(x2)*H.C.F(x2) = 14*23 = 322.

So answer = 322.

Khushi said:   4 years ago
Number 1 = a * 23
number 2 = b * 23
And other factors of LCM are 13 and 14
So clearly a * b = 13 * 14

But my point is:
a * b = 26 * 7
a * b = 81 * 2
As they are co prime in themselves,
So why is the answer not 23*81? Please explain.
(2)

Murali Banerjee said:   9 years ago
It's very simple. Without any calculation, it can easily be solved. Look at numbers.

13 & 14, the last digit of them are 3 & 4. All numbers. Except 322 are not divisible by 14. Hence 322 is the required number.

Palanivel said:   9 years ago
In my view, x and why are given two numbers.

Hcf of (x, y) =23;.
Lcm of (x, y) =13, 14;.

We know that;

Hcf x lcm=X x Y.
So, 23x13=299;.

23 x 14 =322 which is larger so 322 is the answer.

If any mistakes correct me.

Ramesh said:   1 decade ago
I think the two numbers can be 23 and 23x13x14 i e 4186. Is it possible?
Suppose we take two numbers 4 and 24. Their HCF is 4 and LCM is 24. Then the greatest number is 24 itself even though it is the LCM.Am I right?

Pratik said:   6 years ago
I will explain to you with Example.
Take two numbers 21 & 36.
21 - 7 *3 & 36 - 12 *3.
H.C.F. - 3.
They gave H.C.F. and give two factors of L.C.M. 7 and 12.
Okey now simply apply logic which is greater.
(1)

Striker said:   1 decade ago
H.C.F. = 23 and L.C.M. are 13 and 14. So if HCF is 23 then two numbers can be 23x and 23y And as given LCM are 13 &14 we know HCF*LCM=x*y so from that 23*13 and 23*14 are two number and greater one is 23*14.

Aumshesh Upparwar said:   6 years ago
See for any number there are 1 HCF and 1 LCM.
So remember this formula:

HCF * LCM= N1 + N2.

HCF given 23;
And LCM given 13&14.
1st take 23*13= N1*N2.
Then take 24*14= N1*N2.
HIGHEST IS THE ANSWER.


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