Tips and Tricks for LCM
On this page you will become familiar with Tips And Tricks And Shortcuts of LCM and also get some formulas to solve LCM Questions Quickly.
Definition :Least Common Multiple (LCM) is smallest positive integer which is is a multiple of two or more numbers. LCM is also known Lowest Common Multiple.
LCM Tricks and Shortcuts
Trick to find the LCM of any number.
Step 1 : Take the multiple of the highest number among the numbers of which you have to find the LCM.
Step 2 : Continue on multiplying till you get a number which is divisible by all three.
Step 3 : The number which is divisible by all the three numbers and also is a multiple of the highest digit among them is the LCM of he number.
Find the LCM of 12, 24 and 30
- Multiple of 30 = 30, 60, 90, 120.
- Among these four number 120 is the only number which is divisible by all the three number.
Definition and Formulas
Factorization Method:
Resolve each one of the given numbers into a product of prime factors. Then, L.C.M. is the product of the highest powers of all the factors.
Example : Find out LCM of 8 and 14
Express each number as a product of prime factors. (Reference: Prime Factorization)
8 = 2 × 2 × 2
14 = 2 × 7
LCM = The product of highest powers of all prime factors.
Here the prime factors are 2 and 7
The highest power of 2 here = 3
The highest power of 7 here = 1
Hence LCM = 2× 2× 2 × 7 = 56
Division Method (short-cut):
Arrange the given numbers in a row in any order. Divide by a number which divides exactly at least two of the given numbers and carry forward the numbers which are not divisible. Repeat the above process till no two of the numbers are divisible by the same number except 1. The product of the divisors and the undivided numbers is the required L.C.M. of the given numbers.
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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