Calculate the Least Common Multiple or LCM of 75, 105, 110 and 117
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The instructions to find the LCM of 75, 105, 110 and 117 are the next:
1. Decompose all numbers into prime factors
| 75 | 3 |
| 25 | 5 |
| 5 | 5 |
| 1 |
| 105 | 3 |
| 35 | 5 |
| 7 | 7 |
| 1 |
| 110 | 2 |
| 55 | 5 |
| 11 | 11 |
| 1 |
| 117 | 3 |
| 39 | 3 |
| 13 | 13 |
| 1 |
2. Write all numbers as the product of its prime factors
| Prime factors of 75 | = | 3 . 52 |
| Prime factors of 105 | = | 3 . 5 . 7 |
| Prime factors of 110 | = | 2 . 5 . 11 |
| Prime factors of 117 | = | 32 . 13 |
3. Choose the common and uncommon prime factors with the greatest exponent
Common prime factors: None
Common prime factors with the greatest exponent: None
Uncommon prime factors: 3 , 5 , 7 , 2 , 11 , 13
Uncommon prime factors with the greatest exponent: 32, 52, 71, 21, 111, 131
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 = 32. 52. 71. 21. 111. 131 = 450450
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