Question
Find Least Common Multiple of 70, 110 and 150 using prime factorisation method.
Answer
LCM( 70, 110, 150 ) = 11550
Explanation
Step 1: Write down factorisation of each number:
70 = 2 · 5 · 7
110 = 2 · 5 · 11
150 = 2 · 3 · 5 · 5
Step 2 : Match primes vertically:
| 70 | = | 2 | · | 5 | · | 7 | ||||||
| 110 | = | 2 | · | 5 | · | 11 | ||||||
| 150 | = | 2 | · | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 70 | = | 2 | · | 5 | · | 7 | ||||||||
| 110 | = | 2 | · | 5 | · | 11 | ||||||||
| 150 | = | 2 | · | 3 | · | 5 | · | 5 | ||||||
| LCM | = | 2 | · | 3 | · | 5 | · | 5 | · | 7 | · | 11 | = | 11550 |
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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