Calculate the Least Common Multiple or LCM of 40, 100 and 180
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The instructions to find the LCM of 40, 100 and 180 are the next:
1. Decompose all numbers into prime factors
| 40 | 2 |
| 20 | 2 |
| 10 | 2 |
| 5 | 5 |
| 1 |
| 100 | 2 |
| 50 | 2 |
| 25 | 5 |
| 5 | 5 |
| 1 |
| 180 | 2 |
| 90 | 2 |
| 45 | 3 |
| 15 | 3 |
| 5 | 5 |
| 1 |
2. Write all numbers as the product of its prime factors
| Prime factors of 40 | = | 23 . 5 |
| Prime factors of 100 | = | 22 . 52 |
| Prime factors of 180 | = | 22 . 32 . 5 |
3. Choose the common and uncommon prime factors with the greatest exponent
Common prime factors: 2 , 5
Common prime factors with the greatest exponent: 23, 52
Uncommon prime factors: 3
Uncommon prime factors with the greatest exponent: 32
4. Calculate the Least Common Multiple or LCM
Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.
LCM = 23. 52. 32 = 1800
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