What is the lowest common multiple of 12 and 9?

The lowest common multiple (LCM) of 12 and 9 is 36.

To find the LCM, we can start by listing the multiples of each number:

• Multiples of 12: 12, 24, 36, 48, 60, …
• Multiples of 9: 9, 18, 27, 36, 45, …

Now, we look for the smallest multiple that appears in both lists. As we can see, 36 is the first common multiple of both 12 and 9.

Alternatively, we can also use the prime factorization method:

• 12 = 2² × 3
• 9 = 3²

To find the LCM, we take the highest power of each prime number that appears in the factorizations:

• For 2, the highest power is 2² (from 12).
• For 3, the highest power is 3² (from 9).

Now we multiply these together:

LCM = 2² × 3² = 4 × 9 = 36.

Thus, the lowest common multiple of 12 and 9 is 36.