Question
Find Least Common Multiple of 36, 25 and 62 using prime factorisation method.
Answer
LCM( 36, 25, 62 ) = 27900
Explanation
Step 1: Write down factorisation of each number:
36 = 2 · 2 · 3 · 3
25 = 5 · 5
62 = 2 · 31
Step 2 : Match primes vertically:
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||
| 25 | = | 5 | · | 5 | ||||||||||
| 62 | = | 2 | · | 31 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||||
| 25 | = | 5 | · | 5 | ||||||||||||
| 62 | = | 2 | · | 31 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | · | 31 | = | 27900 |
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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