167
Question
Find the lcm by prime factorization
75,150,200
75,150,200
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Solution
The instructions to find the LCM of 75, 150 and 200 are the next:
1. Decompose all numbers into prime factors 75 3 25 5 5 5 1
150 2 75 3 25 5 5 5 1
200 2 100 2 50 2 25 5 5 5 1
2. Write all numbers as the product of its prime factors Prime factors of 75 = 3 . 52 Prime factors of 150 = 2 . 3 . 52 Prime factors of 200 = 23 . 52
3. Choose the common and uncommon prime factors with the greatest exponent Common prime factors: 5
Common prime factors with the greatest exponent: 52
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. 31. 23 = 600
The instructions to find the LCM of 75, 150 and 200 are the next:
1. Decompose all numbers into prime factors| 75 | 3 |
| 25 | 5 |
| 5 | 5 |
| 1 |
| 150 | 2 |
| 75 | 3 |
| 25 | 5 |
| 5 | 5 |
| 1 |
| 200 | 2 |
| 100 | 2 |
| 50 | 2 |
| 25 | 5 |
| 5 | 5 |
| 1 |
| Prime factors of 75 | = | 3 . 52 |
| Prime factors of 150 | = | 2 . 3 . 52 |
| Prime factors of 200 | = | 23 . 52 |
Common prime factors: 5
Common prime factors with the greatest exponent: 52
Uncommon prime factors: 3 , 2
Uncommon prime factors with the greatest exponent: 31, 23
4. Calculate the Least Common Multiple or LCMRemember, 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. 31. 23 = 600
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