What is the LCM of
1. 9, 12, and 20
2. 9, 21, and 63
3. 10, 20, and 45
THANK YOU!!!!!!!!!!!!
To find the least common multiple (LCM) of a set of numbers, we need to find the smallest number that is divisible by all of the given numbers.
1. LCM of 9, 12, and 20:
- Start by listing the prime factors of each number:
9 = 3 * 3
12 = 2 * 2 * 3
20 = 2 * 2 * 5
- Now, determine the highest power of each unique prime factor:
2^2 * 3^2 * 5^1 = 180
- The LCM of 9, 12, and 20 is 180.
2. LCM of 9, 21, and 63:
- List the prime factors:
9 = 3 * 3
21 = 3 * 7
63 = 3 * 3 * 7
- Determine the highest power of each prime factor:
3^2 * 7^1 = 63
- The LCM of 9, 21, and 63 is 63.
3. LCM of 10, 20, and 45:
- List the prime factors:
10 = 2 * 5
20 = 2 * 2 * 5
45 = 3 * 3 * 5
- Determine the highest power of each prime factor:
2^2 * 3^2 * 5^1 = 180
- The LCM of 10, 20, and 45 is 180.
In conclusion:
1. The LCM of 9, 12, and 20 is 180.
2. The LCM of 9, 21, and 63 is 63.
3. The LCM of 10, 20, and 45 is 180.