Calculate the Least Common Multiple or LCM of 21, 45, 72 and 84
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The instructions to find the LCM of 21, 45, 72 and 84 are the next:
1. Decompose all numbers into prime factors
| 21 | 3 |
| 7 | 7 |
| 1 |
| 45 | 3 |
| 15 | 3 |
| 5 | 5 |
| 1 |
| 72 | 2 |
| 36 | 2 |
| 18 | 2 |
| 9 | 3 |
| 3 | 3 |
| 1 |
| 84 | 2 |
| 42 | 2 |
| 21 | 3 |
| 7 | 7 |
| 1 |
2. Write all numbers as the product of its prime factors
| Prime factors of 21 | = | 3 . 7 |
| Prime factors of 45 | = | 32 . 5 |
| Prime factors of 72 | = | 23 . 32 |
| Prime factors of 84 | = | 22 . 3 . 7 |
3. Choose the common and uncommon prime factors with the greatest exponent
Common prime factors: 3
Common prime factors with the greatest exponent: 32
Uncommon prime factors: 7 , 5 , 2
Uncommon prime factors with the greatest exponent: 71, 51, 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 = 32. 71. 51. 23 = 2520
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