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

Let r be the remainder then the numbers (1305 - r) , (4665 - r) and (6905 - r) are exactly divisible by the required greatest number N.

We know that if two numbers are divisible by a certain number, then their difference is also divisible by that number.

Hence, the numbers.

(4665 - r) - (1305 - r) = (4665 - 1305),
(6905 - r) - (4665 - r) = (6905 - 4665),
(6905 - r) - (1305 - r) = (6905 - 1305).

They are divisible by the required number.

Therefore, the greatest number N = HCF of (4665 - 1305), (6905 - 4665) and (6905 - 1305).

The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder is,

Answer LCM of 5, 6, 7, 8 = 840.

Required number is of the form 840k + 3.

Least value of k for which (840k + 3) is divisible by 9 is k = 2.

Required number = (840 x 2 + 3) = 1683.

My question how to find out K value in this question.

What is the HCF of no's 1365, 4665, 6905?

Anyone explain how the sum of digits in N = (1 + 1 + 2 + 0) = 4?

I Can't understand the N value, please explain the sum of digits N = (1 + 1 + 2 + 0) = 4?

Will you explain the below?

3360:2240:5600.

1120:1120:1120.

How we got this 1120 in common.

Thanks @Saraswati.

How (1 + 1 + 2 + 0)?

Please tell me.

Thanks for excellent explanation @Yogesh.

Thanks for this complete explanation @M. Harish and @Srinivas.