# Tips Tricks and Shortcuts To Solve HCF & LCM

Here, are some easy tips and tricks for you to solve HCF and LCM questions quickly, easily, and efficiently in competitive exams.

## HCF and LCM Tips and Tricks and Shortcuts

• The H.C.F of two or more numbers is smaller than or equal to the smallest number of given numbers
• The smallest number which is exactly divisible by a, b and c is L.C.M of a, b, c.
• The L.C.M of two or more numbers is greater than or equal to the greatest number of given numbers.
• The smallest number which when divided by a, b and c leaves a remainder R in each case. Required number = (L.C.M of a, b, c) + R
• The greatest number which divides a, b and c to leave the remainder R is H.C.F of (a – R), (b – R) and (c – R)
• The greatest number which divide x, y, z to leave remainders a, b, c is H.C.F of (x – a), (y – b) and (z – c)
• The smallest number which when divided by x, y and z leaves remainder of a, b, c (x – a), (y – b), (z – c) are multiples of M
Required number = (L.C.M of x, y and z) – M ## Type 1: Tips and Tricks and Shortcuts. Find the greatest or smallest number

### Question 1.

Find the greatest 5 digit number divisible by 5, 15, 20, and 25

Options

1. 99900
2. 99000
3. 99990
4. 90990

#### Solution:

LCM of 5, 15, 20, and 25 is 300

The greatest 5 digit number is 99999

99999/300 = 99

Therefore, required number 99999 – 99 = 99900

## Type 2: Find the numbers, sum of numbers, product of numbers if

1. Their ratio and H.C.F. are given.
2. Product of H.C.F. and L.C.M are given

### Question 2.

The product of two numbers is 3888. If the H.C.F. of these numbers is 36, then the greater number is:

Options

1. 110
2. 108
3. 36
4. 120

#### Solution:

Let the two numbers be 36x and 36y

Now, 36x * 36y = 3888

xy = 3888/36 * 36

xy = 3

Now, co-primes with product 3 are (1, 3).

Therefore, the required numbers are 36 * 1 = 36

36 * 3 = 108

Therefore the greatest number is 108

## Tips and Tricks and Shortcuts to find HCF easily

### Ques. 3

Find HCF of 12 and 16.

Options

(A) 5
(B) 4
(C) 12
(D) 16

#### Correct Option(B)

Solution

Find the difference between 12 and 16. The difference is 4. Now, check whether the numbers are divisible by the difference. 12 is divisible by 4 and 16 is divisible by 4.Hence, the HCF is 4.

### Ques. 4

Find HCF of 18 and 22.

Options
(A) 2
(B) 4
(C) 18
(D) 36

#### Solution

Find the difference between 18 and 22. The difference is 4. Now, check whether the numbers are divisible by the difference. Both 18 and 22 are not divisible by 4. So take the factors of the difference. The factors of 4 are 2*2*1. Now, check whether the numbers are divisible by the factors. 18 and 22 are divisible by factor 2.

Hence, the HCF is 2.

Note: If there are more than two numbers, take the least difference.

## Tips and Tricks and Shortcuts to find LCM easily

### Ques 5

Find LCM of 2,4,8,16.

Options
(A) 16
(B) 18
(C) 12
(D) 2

#### Solution

Factorize of above number
2 =2
8 = 23
16 = 24

Choose the largest number. In this example, the largest number is 16. Check whether 16 is divisible by all other remaining numbers. 16 is divisible by 2, 4, 8. Hence, the LCM is 16.

## Tips and Tricks and Shortcuts to find LCM easily

### Ques 6

Find the LCM of 2,3,7,21.

Options
(A)
21
(B)
44
(C)
36
(D)
42

#### Solution

Choose the largest number. The largest number is 21. Check whether 21 is divisible by all other remaining numbers. 21 is divisible by 3 and 7 but not by 2. So multiply 21 and 2. The result is 42. Now, check whether 42 is divisible by 2, 3, 7. Yes, 42 is divisible. Hence, the LCM is 42.