Lowest common multiple
Definition
The Lowest Common Multiples of two or
more numbers is the least or smallest number that all the given number can divide without a remainder.

Example1: Find the LCM of 8 and 12
Step1: List the multiples of 8 and 12
8: 8, 16, 24, 32, 48, 54…
12: 12, 24, 36, 48…
Common multiples are 24, 48…
LCM =24

LCM BY PRIME FACTORIZATION METHOD
Steps involved
1. Express the number as product of its prime factors in index form
2. Take all prime factors with highest index or powers
3. multiply them
Example1 : find the LCM of 12 and 18 by prime factorization method
12 = 2 x 2 x 3 = 22 x 31
18= 2 x 3 x 3 = 21 x 32
Highest factors = 22 x 32 = 36

DIVISION LADDER METHOD
Example1: find the LCM OF 24 and 36

2   24   36                                                                                     

2   12  18

2    6     9

2    3     9

3   1     3 

3   1      1


POINT TO NOTE
1. LCM is always greater than or equal to the larger number
2 when LCM is multiplied with HCF it give the product of the numbers.

PRACTICE QUESTIONS
1. find the LCM of 15 and 18
2. find the LCM of 24 and 60
3. Find the LCM OF 25 and 40 using prime
factorization method.
4. Two industrial machines produce a
product at intervals. Machine A produces every 16 hours, machine Y every 20 hours . If the they both start at 10:00am, when will they produce together?

You may also want to learn about Highest Common Factor (HCF)