Find Least Common Multiple of 39375 and 19490625 using prime factorisation method.
Answer
LCM( 39375, 19490625 ) = 19490625
Explanation
Step 1: Write down factorisation of each number:
39375 = 3 · 3 · 5 · 5 · 5 · 5 · 7
19490625 = 3 · 3 · 3 · 3 · 5 · 5 · 5 · 5 · 5 · 7 · 11
Step 2 : Match primes vertically:
| 39375 | = | 3 | · | 3 | · | 5 | · | 5 | · | 5 | · | 5 | · | 7 | ||||||||
| 19490625 | = | 3 | · | 3 | · | 3 | · | 3 | · | 5 | · | 5 | · | 5 | · | 5 | · | 5 | · | 7 | · | 11 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 39375 | = | 3 | · | 3 | · | 5 | · | 5 | · | 5 | · | 5 | · | 7 | ||||||||||
| 19490625 | = | 3 | · | 3 | · | 3 | · | 3 | · | 5 | · | 5 | · | 5 | · | 5 | · | 5 | · | 7 | · | 11 | ||
| LCM | = | 3 | · | 3 | · | 3 | · | 3 | · | 5 | · | 5 | · | 5 | · | 5 | · | 5 | · | 7 | · | 11 | = | 19490625 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.
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