text: 23 June, 12:22
  
  Find the least common multiple of (2a-1) 2, 1-4a2, and 8a3-12a2+6a-1
  
  0
  1. 23 June, 13:57
  0
  The LCM = - 2 (8a3 - 12a2 + 6a - 1).
  
  Step-by-step explanation:
  
  Least common multiple (LCM) of numbers is list the prime factors of each number, then multiply each factor by the greatest number of times it occurs in all the choosen numbers. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.
  
  (2a - 1) 2:
  
  = 2 * (2a - 1).
  
  1 - 4a2:
  
  -1 * (4a2 - 1) = - 1 * (a2 - 1/4).
  
  -1 * (a - 1/2) ^2
  
  = - 1 * (2a - 1) ^2
  
  8a3 - 12a2 + 6a - 1:
  
  Inputting a = 1/2,
  
  1 - 3 + 3 - 1 = 0
  
  So 2a - 1 is a root, dividing its root by the equation,
  
  (2a - 1) (4a2 - 4a + 1)
  
  Inputting 2a - 1 into 4a2 - 4a + 1,
  
  1 - 2 + 1 = 0.
  
  So 2a - 1 is a root, dividing its root by the equation,
  
  (2a - 1) (2a - 1)
  
  Therefore, 8a3 - 12a2 + 6a - 1 = (2a - 1) ^3
  
  The LCM = - 2 (8a3 - 12a2 + 6a - 1)
explanation: The document contains a math question and a detailed step-by-step answer to the question. The question asks for the least common multiple (LCM) of the expressions (2a-1)², 1-4a², and 8a³-12a²+6a-1. The answer provides a detailed explanation of how to find the LCM, including factorization and polynomial division.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: 23 June, 12:22
  
  Find the least common multiple of (2a-1) 2, 1-4a2, and 8a3-12a2+6a-1
  
  0
  1. 23 June, 13:57
  0
  The LCM = - 2 (8a3 - 12a2 + 6a - 1).
  
  Step-by-step explanation:
  
  Least common multiple (LCM) of numbers is list the prime factors of each number, then multiply each factor by the greatest number of times it occurs in all the choosen numbers. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.
  
  (2a - 1) 2:
  
  = 2 * (2a - 1).
  
  1 - 4a2:
  
  -1 * (4a2 - 1) = - 1 * (a2 - 1/4).
  
  -1 * (a - 1/2) ^2
  
  = - 1 * (2a - 1) ^2
  
  8a3 - 12a2 + 6a - 1:
  
  Inputting a = 1/2,
  
  1 - 3 + 3 - 1 = 0
  
  So 2a - 1 is a root, dividing its root by the equation,
  
  (2a - 1) (4a2 - 4a + 1)
  
  Inputting 2a - 1 into 4a2 - 4a + 1,
  
  1 - 2 + 1 = 0.
  
  So 2a - 1 is a root, dividing its root by the equation,
  
  (2a - 1) (2a - 1)
  
  Therefore, 8a3 - 12a2 + 6a - 1 = (2a - 1) ^3
  
  The LCM = - 2 (8a3 - 12a2 + 6a - 1)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and a detailed step-by-step answer to the question. The question asks for the least common multiple (LCM) of the expressions (2a-1)², 1-4a², and 8a³-12a²+6a-1. The answer provides a detailed explanation of how to find the LCM, including factorization and polynomial division.
  
  Label: question-and-answer