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

Thnks @Sanchay.

We subtracted 1305 from 4665, 4665 from 6905 and 1305 from 6905 because we needed n as a common factor which can be obtained this way.

Let us consider 1305 as q1
4665 as q2
And 6905 as we
Then,

4665-1305 = N(q2 -q1).
6905-4665 = N(q3-q2 ).
6905-1305 = N(q3-q2 ).

Now we get here N as the factor of all 3 digits and we need to find the greatest factor so, take out the HCF of all three numbers i.e 1305, 4665, 6905 = 1120.

And this is your answer if your question asks no. Of digits in the number simply add the digits i.e 1+1+2+0=4.

Hope this helped.

Can we try it in this way?

3+3+6+0= 12
2+2+4+0= 8,
5+6+0+0= 11,
12+8+11= 31,
3+1= 4.

Thanks @Prakash.

Thanks @Yogesh.

@Saraswati.

I can't understand why you are multiplying 10?

Please explain it.

When you divide 1305, 4665 and 6905 by 1120 you will get the same remainder 185 so N is 1120 so the sum of the digits is 1+1+2+0=4.

What if the question is for finding smallest such number? Is it same like we have to find lcm of difference between numbers?

Subtract the numbers such as,

4665-1305 = 3360 and 6905 - 4665 = 2240 then subtracting the obtained results.

3360-2240 = 1120. Therefore 1 + 1 + 2 + 0 = 4.

N(q2-q1)=(4665-1305)=3360
N(q3-q2)=(6905-4665)=2240
N(q3-q1)=(6905-1305)=5600

N(q1+q2+q3)=3360+2240+5600=11200

N(1+1+2+0+0)=4.