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Question

Find the lcm by prime factorization
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


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