LCM( 294, 441, 735 ) = 4410
Step 1: Write down factorisation of each number:
294 = 2 · 3 · 7 · 7
441 = 3 · 3 · 7 · 7
735 = 3 · 5 · 7 · 7
Step 2 : Match primes vertically:
294 | = | 2 | · | 3 | · | 7 | · | 7 | ||||
441 | = | 3 | · | 3 | · | 7 | · | 7 | ||||
735 | = | 3 | · | 5 | · | 7 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
294 | = | 2 | · | 3 | · | 7 | · | 7 | ||||||
441 | = | 3 | · | 3 | · | 7 | · | 7 | ||||||
735 | = | 3 | · | 5 | · | 7 | · | 7 | ||||||
LCM | = | 2 | · | 3 | · | 3 | · | 5 | · | 7 | · | 7 | = | 4410 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.