Calculate the Least Common Multiple or LCM of 105, 175 and 280
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The instructions to find the LCM of 105, 175 and 280 are the next:
1. Decompose all numbers into prime factors
| 105 | 3 |
| 35 | 5 |
| 7 | 7 |
| 1 |
| 175 | 5 |
| 35 | 5 |
| 7 | 7 |
| 1 |
| 280 | 2 |
| 140 | 2 |
| 70 | 2 |
| 35 | 5 |
| 7 | 7 |
| 1 |
2. Write all numbers as the product of its prime factors
| Prime factors of 105 | = | 3 . 5 . 7 |
| Prime factors of 175 | = | 52 . 7 |
| Prime factors of 280 | = | 23 . 5 . 7 |
3. Choose the common and uncommon prime factors with the greatest exponent
Common prime factors: 5 , 7
Common prime factors with the greatest exponent: 52, 71
Uncommon prime factors: 3 , 2
Uncommon prime factors with the greatest exponent: 31, 23
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 = 52. 71. 31. 23 = 4200
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