We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.More informationAgree
ad

Least Common Multiple (LCM)

Least Common Multiple (LCM) of two or more numbers is the smallest number that is a multiple of all the numbers.

Example: LCM of 3 and 4 = 12 because 12 is the smallest number which is a multiple of both 3 and 4 (In other words, 12 is the smallest number which is divisible by both 3 and 4).

We can find LCM using prime factorization method or division method.

How to find out LCM using prime factorization method

Step 1 : Express each number as a product of prime factors.

Step 2 : LCM = The product of highest powers of all prime factors.

Example 1: Find out LCM of 8 and 14

Step 1 : Express each number as a product of prime factors. (Reference: Prime Factorization)

8 = 23

14 = 2 × 7

Step 2 : LCM = The product of highest powers of all prime factors.

Here the prime factors are 2 and 7

The highest power of 2 here = 23

The highest power of 7 here = 7

Hence LCM = 23 × 7 = 56 Example 2: Find out LCM of 18, 24, 9, 36 and 90

Step 1 : Express each number as a product of prime factors.

18 = 2 × 32

24 = 23 × 3

9 = 32

36 = 23 × 32

90 = 2 × 5 × 32

Step 2 : LCM = The product of highest powers of all prime factors.

Here the prime factors are 2, 3 and 5

The highest power of 2 here = 23

The highest power of 3 here = 32

The highest power of 5 here = 5

Hence LCM = 23 × 32 × 5 = 360

How to find out LCM using division Method (shortcut method)

Step 1: Write the given numbers in a horizontal line separated by commas.

Step 2: Divide the given numbers by the smallest prime number which can exactly divide at least two of the given numbers.

Step 3: Write the quotients and undivided numbers in a line below the first.

Step 4: Repeat the process until we reach a stage where no prime factor is common to any two numbers in the row.

Step 5: LCM = The product of all the divisors and the numbers in the last line.

Example 1: Find out LCM of 8 and 14
28,14
4,7

Hence Least common multiple (L.C.M) of 8 and 14
= 2 × 4 × 7
= 56 Example 2: Find out LCM of 18, 24, 9, 36 and 90

218,24,9,36,90
29,12,9,18,45
39,6,9,9,45
33,2,3,3,15
1,2,1,1,5

Hence Least common multiple (L.C.M) of 18, 24, 9, 36 and 90
= 2 × 2 × 3 × 3 × 2 × 5
= 360

Add Your Comment

(use Q&A for new questions)
?
Name
cancel
preview