Find Least Common Multiple of 72, 49 and 53 using prime factorisation method.
Answer
LCM( 72, 49, 53 ) = 186984
Explanation
Step 1: Write down factorisation of each number:
72 = 2 · 2 · 2 · 3 · 3
49 = 7 · 7
53 = 53
Step 2 : Match primes vertically:
| 72 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||
| 49 | = | 7 | · | 7 | ||||||||||||
| 53 | = | 53 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 72 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||||
| 49 | = | 7 | · | 7 | ||||||||||||||
| 53 | = | 53 | ||||||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 7 | · | 7 | · | 53 | = | 186984 |
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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