Tips And Tricks And-Shortcuts of LCM

May 29, 2023

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.

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

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