Calculate the Least Common Multiple or LCM of 30, 85, 100 and 112
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The instructions to find the LCM of 30, 85, 100 and 112 are the next:
1. Decompose all numbers into prime factors
| 30 | 2 |
| 15 | 3 |
| 5 | 5 |
| 1 |
| 85 | 5 |
| 17 | 17 |
| 1 |
| 100 | 2 |
| 50 | 2 |
| 25 | 5 |
| 5 | 5 |
| 1 |
| 112 | 2 |
| 56 | 2 |
| 28 | 2 |
| 14 | 2 |
| 7 | 7 |
| 1 |
2. Write all numbers as the product of its prime factors
| Prime factors of 30 | = | 2 . 3 . 5 |
| Prime factors of 85 | = | 5 . 17 |
| Prime factors of 100 | = | 22 . 52 |
| Prime factors of 112 | = | 24 . 7 |
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: 2 , 3 , 5 , 17 , 7
Uncommon prime factors with the greatest exponent: 24, 31, 52, 171, 71
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 = 24. 31. 52. 171. 71 = 142800
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