Question
Find Least Common Multiple of 3750, 193117 and 950 using prime factorisation method.
Answer
LCM( 3750, 193117, 950 ) = 13759586250
Explanation
Step 1: Write down factorisation of each number:
3750 = 2 · 3 · 5 · 5 · 5 · 5
193117 = 113 · 1709
950 = 2 · 5 · 5 · 19
Step 2 : Match primes vertically:
| 3750 | = | 2 | · | 3 | · | 5 | · | 5 | · | 5 | · | 5 | ||||||
| 193117 | = | 113 | · | 1709 | ||||||||||||||
| 950 | = | 2 | · | 5 | · | 5 | · | 19 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 3750 | = | 2 | · | 3 | · | 5 | · | 5 | · | 5 | · | 5 | ||||||||
| 193117 | = | 113 | · | 1709 | ||||||||||||||||
| 950 | = | 2 | · | 5 | · | 5 | · | 19 | ||||||||||||
| LCM | = | 2 | · | 3 | · | 5 | · | 5 | · | 5 | · | 5 | · | 19 | · | 113 | · | 1709 | = | 13759586250 |
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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