**LCM HCF Divisibility Questions Trick**: Here you can check shortcut trick to solve questions based on LCM & HCF division. In various competitive exams, questions like "

**find the least number which when devided by x, leaves remainder y**". The solution to these problems is quite easy if you know the proper basic method. It takes a little time to find the solution to these problems. Here you can check solution to these type of problems with examples.

The solution is explained here with example.

## LCM HCM Based Questions Method of Solution

**Example: 1.**

Find the least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3:

Solution:

First we have to find the LCM of 5, 6, 4 and 3.

5 = 5

6 = 2, 3

4 = 2, 2

3 = 3

So L.C.M. of 5, 6, 4 and 3 = 60.

When we divide 2497 by 60, we find that the remainder is 37.

So the Number that to be added = 60 - 37 = 23.

**Example: 2.**

Find the least number which when increased by 5 is divisible by 24, 32, 36 and 54 each.

Solution:

First we have to find the LCM of 24, 32, 36, 54

24 = 2, 2, 2, 3

32 = 2, 2, 2, 2, 2

36 = 2, 2, 3, 3

54 = 2, 3, 3, 3

So LCM = 864

So Required number = (L.C.M. of 24, 32, 36, 54) - 5 = 864 - 5 = 859.

**Example: 3.**

Find the least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18.

Solution:

First Find LCM.

6 = 2, 3

9 = 3, 3

15 = 3, 5

18 = 2, 3, 3

LCM of 6, 9, 15 and 18 is 90.

Let required number be 90x + 4, which is a multiple of 7.

The Least value of k for which (90x + 4) is divisible by 7 is k = 4.

So the Required number is = (90*4) + 4 = 364.

**Example: 4.**

Find the least multiple of 23 which when devided by 18, 21 and 24 leaves a remainder 7, 10, 13 respectively.

Solution:

First we have to find the LCM of 18, 21 & 24.

18 = 2 × 3 × 3

21 = 3 × 7

24 = 2 × 2 × 2 × 3

So LCM of 18, 21 & 24 = 504

Now check the given numbers remainder respectively.

18-7=11

21-10=11

24-13=11

We find it that there is 11 difference in each number.

Now the formula is

Required Number = LCM*X-11

Required Number = 504*X-11

by Hit & Trial method:

when putting X=6

We get

Required number = 3013 Ans.