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What is the least common multiple of 12, 18, and 30?

User Cachapa
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Final answer:

The least common multiple of 12, 18, and 30 is calculated using prime factorization, with the highest powers of all prime factors being taken into account.

Step-by-step explanation:

The least common multiple (LCM) of 12, 18, and 30 needs to be found to determine the smallest number that is a multiple of all three. To find the LCM, we can use the prime factorization method:

  • 12 = 2² × 3
  • 18 = 2 × 3²
  • 30 = 2 × 3 × 5

Now, we take the highest powers of all prime factors that appear in any of the numbers:

LCM = 2² (which is 4) × 3² (which is 9) × 5 = 4 × 9 × 5 = 36 × 5 = 180.

The least common multiple of 12, 18, and 30 is 180. This number is the smallest number that all three numbers can divide into without leaving a remainder.

User Karto
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