Find Least Common Multiple of 32, 46 and 98 using prime factorisation method.
Answer
LCM( 32, 46, 98 ) = 36064
Explanation
Step 1: Write down factorisation of each number:
32 = 2 · 2 · 2 · 2 · 2
46 = 2 · 23
98 = 2 · 7 · 7
Step 2 : Match primes vertically:
| 32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||
| 46 | = | 2 | · | 23 | ||||||||||||
| 98 | = | 2 | · | 7 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||||
| 46 | = | 2 | · | 23 | ||||||||||||||
| 98 | = | 2 | · | 7 | · | 7 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 7 | · | 7 | · | 23 | = | 36064 |
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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