Find Least Common Multiple of 250, 148 and 316 using prime factorisation method.
Answer
LCM( 250, 148, 316 ) = 1461500
Explanation
Step 1: Write down factorisation of each number:
250 = 2 · 5 · 5 · 5
148 = 2 · 2 · 37
316 = 2 · 2 · 79
Step 2 : Match primes vertically:
| 250 | = | 2 | · | 5 | · | 5 | · | 5 | ||||||
| 148 | = | 2 | · | 2 | · | 37 | ||||||||
| 316 | = | 2 | · | 2 | · | 79 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 250 | = | 2 | · | 5 | · | 5 | · | 5 | ||||||||
| 148 | = | 2 | · | 2 | · | 37 | ||||||||||
| 316 | = | 2 | · | 2 | · | 79 | ||||||||||
| LCM | = | 2 | · | 2 | · | 5 | · | 5 | · | 5 | · | 37 | · | 79 | = | 1461500 |
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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