LCM( 26, 38, 112 ) = 27664
Step 1: Write down factorisation of each number:
26 = 2 · 13
38 = 2 · 19
112 = 2 · 2 · 2 · 2 · 7
Step 2 : Match primes vertically:
26 | = | 2 | · | 13 | ||||||||||
38 | = | 2 | · | 19 | ||||||||||
112 | = | 2 | · | 2 | · | 2 | · | 2 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
26 | = | 2 | · | 13 | ||||||||||||
38 | = | 2 | · | 19 | ||||||||||||
112 | = | 2 | · | 2 | · | 2 | · | 2 | · | 7 | ||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 7 | · | 13 | · | 19 | = | 27664 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.