Find the least common multiple.

12 and 5

1 answer

To find the least common multiple (LCM) of 12 and 5, we can use the following steps:

  1. List the prime factors of each number:

    • The prime factorization of 12 is \(2^2 \times 3^1\).
    • The prime factorization of 5 is \(5^1\).
  2. Identify all the prime factors:

    • The unique prime factors from both numbers are 2, 3, and 5.
  3. Take the highest power of each prime factor:

    • For 2, the highest power is \(2^2\) (from 12).
    • For 3, the highest power is \(3^1\) (from 12).
    • For 5, the highest power is \(5^1\) (from 5).
  4. Multiply these together to get the LCM: \[ LCM = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 \]

  5. Calculate the product: \[ 4 \times 3 = 12 \] \[ 12 \times 5 = 60 \]

Thus, the least common multiple of 12 and 5 is 60.