Calculate the Least Common Multiple or LCM of 45, 80 and 105
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The instructions to find the LCM of 45, 80 and 105 are the next:
1. Decompose all numbers into prime factors
| 45 | 3 |
| 15 | 3 |
| 5 | 5 |
| 1 |
| 80 | 2 |
| 40 | 2 |
| 20 | 2 |
| 10 | 2 |
| 5 | 5 |
| 1 |
| 105 | 3 |
| 35 | 5 |
| 7 | 7 |
| 1 |
2. Write all numbers as the product of its prime factors
| Prime factors of 45 | = | 32 . 5 |
| Prime factors of 80 | = | 24 . 5 |
| Prime factors of 105 | = | 3 . 5 . 7 |
3. Choose the common and uncommon prime factors with the greatest exponent
Common prime factors: 5
Common prime factors with the greatest exponent: 51
Uncommon prime factors: 3 , 2 , 7
Uncommon prime factors with the greatest exponent: 32, 24, 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 = 51. 32. 24. 71 = 5040
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