Find Least Common Multiple of 4032 and 60 using prime factorisation method.
Answer
LCM( 4032, 60 ) = 20160
Explanation
Step 1: Write down factorisation of each number:
4032 = 2 · 2 · 2 · 2 · 2 · 2 · 3 · 3 · 7
60 = 2 · 2 · 3 · 5
Step 2 : Match primes vertically:
| 4032 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 7 | ||
| 60 | = | 2 | · | 2 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 4032 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 7 | ||||
| 60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 7 | = | 20160 |
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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