# Tips And Tricks And-Shortcuts of LCM

## Tips and Tricks for LCM

Least Common Multiple (LCM) is  smallest positive integer whick is  is a multiple of two or more numbers. LCM is also known Lowest Common Multiple. On this page you’ll become familiar with Tips And Tricks And Shortcuts of LCM.

### Tips and Tricks on LCM

• LCM: Least Common Multiple is a number which is multiple of two or more than two numbers.
• Here, are some easy tips and tricks for you to solve LCM questions quickly, easily, and efficiently in competitive exams and other recruitment.
• 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 least 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

### Type 1: Find the least or greatest number

Question 1. The least number which when divided by 15, 20 and 25 leaves a remainder 8 in each case is:

Options

A. 308

B. 304

C. 300

D. 310

Solution     Required number = (L.C.M of 15, 20, 25) + 8 = 300 + 8 = 308.

Correct option:A

### Type 2: Tips and Tricks and Shortcuts to Find LCM

Question 2. Find the LCM of 24, 300.

Options

A. 300

B. 720

C. 600

D. 420

Solution      Prime factorization of 24 = 2 * 2 * 2 * 3 = 23 * 31 * 50

Prime factorization of 300 = 2 * 2 * 3 * 5 = 22 * 31 * 52

Highest exponent value we take = 23 * 31 * 52 =600

Correct option:C

### Find LCM easily with the help of shortcut

Question 3 Find LCM of 2,4,8,16.

Options

(A) 16

(B) 18

(C) 12

(D) 2

Solution      Factorize of above number

2 =2
4 = $2^{2}$
8 = $2^{3}$
16 = $2^{4}$

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, 16. Hence, the LCM is 16.

Correct Option A

Question 4 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.

Correct Options D

Read How to Solve LCM questions quickly.

Formulas for LCM

More questions on LCM