Find the least common multiple of 9, 10, and 30.
The multiples are:
9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108 . . .
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110 . . .
30, 60, 90, 120, 150 . . .
What is the smallest multiple of those three numbers?
i got 90
To find the least common multiple (LCM) of multiple numbers, you can use either prime factorization or the method of finding the LCM by listing multiples. Let's use the prime factorization method:
Step 1: Prime factorize each number:
- 9 = 3 * 3
- 10 = 2 * 5
- 30 = 2 * 3 * 5
Step 2: Identify the highest power of each prime factor:
- The highest power of 2 is 2^1.
- The highest power of 3 is 3^2.
- The highest power of 5 is 5^1.
Step 3: Multiply the highest power of each prime factor together:
- LCM = 2^1 * 3^2 * 5^1
Step 4: Calculate the result:
- LCM = 2 * 9 * 5 = 90
Therefore, the LCM of 9, 10, and 30 is 90.