Find Least Common Multiple of 528, 7 and 1023 using prime factorisation method.
Answer
LCM( 528, 7, 1023 ) = 114576
Explanation
Step 1: Write down factorisation of each number:
528 = 2 · 2 · 2 · 2 · 3 · 11
7 = 7
1023 = 3 · 11 · 31
Step 2 : Match primes vertically:
| 528 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 11 | ||||
| 7 | = | 7 | ||||||||||||||
| 1023 | = | 3 | · | 11 | · | 31 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 528 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 11 | ||||||
| 7 | = | 7 | ||||||||||||||||
| 1023 | = | 3 | · | 11 | · | 31 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 7 | · | 11 | · | 31 | = | 114576 |
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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