LCM(90, 22)
The LCM of 90 and 22 is 990.
To find the least common multiple (LCM) of 90 and 22, you can follow these steps:
Step 1: Write the prime factorization of each number:
90 = 2 × 3² × 5
22 = 2 × 11
Step 2: Identify the highest power of each prime factor that appears in either number's prime factorization:
2 appears in both numbers, so we take the highest power, which is 1.
3 appears only in 90, so it remains as 3.
5 appears only in 90, so it remains as 5.
11 appears only in 22, so it remains as 11.
Step 3: Multiply all the prime factors along with their highest powers:
2 × 3² × 5 × 11 = 330
Therefore, the LCM of 90 and 22 is 330.
To find the least common multiple (LCM) of two numbers, you can use several methods. One approach is to use prime factorization.
First, let's find the prime factorization of each number.
For 90:
Divide 90 by the smallest prime number, 2, repeatedly until you cannot divide evenly anymore: 90 ÷ 2 = 45 ÷ 3 = 15 ÷ 3 = 5.
Therefore, the prime factorization of 90 is 2 × 3 × 3 × 5, or 2^1 × 3^2 × 5^1.
For 22:
Divide 22 by the smallest prime number, 2, repeatedly until you cannot divide evenly anymore: 22 ÷ 2 = 11.
Therefore, the prime factorization of 22 is 2 × 11, or 2^1 × 11^1.
To find the LCM, we take the highest power of each prime factor present in either number and multiply them together.
In this case, the prime factors are 2, 3, 5, and 11. The highest power of each prime factor present is:
- 2^1 (from 90)
- 3^2 (from 90)
- 5^1 (from 90)
- 11^1 (from 22)
So, the LCM of 90 and 22 is 2^1 × 3^2 × 5^1 × 11^1, which is equal to 2 × 3^2 × 5 × 11 = 990.
Therefore, LCM(90, 22) = 990.