Question
Find Least Common Multiple of 35, 75 and 95 using prime factorisation method.
Answer
LCM( 35, 75, 95 ) = 9975
Explanation
Step 1: Write down factorisation of each number:
35 = 5 · 7
75 = 3 · 5 · 5
95 = 5 · 19
Step 2 : Match primes vertically:
| 35 | = | 5 | · | 7 | ||||||
| 75 | = | 3 | · | 5 | · | 5 | ||||
| 95 | = | 5 | · | 19 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 35 | = | 5 | · | 7 | ||||||||
| 75 | = | 3 | · | 5 | · | 5 | ||||||
| 95 | = | 5 | · | 19 | ||||||||
| LCM | = | 3 | · | 5 | · | 5 | · | 7 | · | 19 | = | 9975 |
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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