The LCM of 5a^3 and 60a^2
60 = 5 * 12 so 60 is already a multiple of 5
a^3 = a * a^2 so a^3 is a multiple of a^2
so 60a^3
Why did the math book go to the comedy club? To find the LCMedian! 😄
But in all seriousness, to find the least common multiple (LCM) of 5a^3 and 60a^2, we can break down the factors:
5a^3 = 5 * a * a * a
60a^2 = 2 * 2 * 3 * 5 * a * a
To find the LCM, we need to include all the unique factors with the highest power they appear in. So, the LCM of 5a^3 and 60a^2 is:
2 * 2 * 3 * 5 * a * a * a = 60a^3
To find the least common multiple (LCM) of 5a^3 and 60a^2, we need to consider the highest powers of any common factors.
Step 1: Prime factorize 5a^3 and 60a^2:
- 5a^3 can be written as 5 * a * a * a.
- 60a^2 can be written as 2 * 2 * 3 * 5 * a * a.
Step 2: Identify the highest powers of each prime factor:
- The highest power of 2 is 2 * 2 = 4.
- The highest power of 3 is 3.
- The highest power of 5 is 5.
- The highest power of a is a^3.
Step 3: Multiply the highest powers of each prime factor:
- The LCM of 5a^3 and 60a^2 is 2^4 * 3 * 5 * a^3.
Step 4: Simplify the expression:
- 2^4 * 3 * 5 * a^3 = 16 * 3 * 5 * a^3.
- Multiplying the numbers, we get 240 * a^3.
Therefore, the LCM of 5a^3 and 60a^2 is 240a^3.
To find the least common multiple (LCM) of 5a^3 and 60a^2, you need to determine the highest power of each factor that appears in either number.
Let's break down each term:
For 5a^3:
- The factor 5 appears once.
- The factor a appears three times (a^3).
For 60a^2:
- The factor 2 appears three times (2^3).
- The factor 3 appears once.
- The factor a appears two times (a^2).
Now, take the highest power of each factor that appears in either number:
- The factor 2 appears three times in 60a^2.
- The factor 3 appears once in 60a^2.
- The factor 5 appears once in 5a^3.
- The factor a appears three times in 5a^3.
Therefore, the LCM of 5a^3 and 60a^2 is 2^3 * 3 * 5 * a^3, which simplifies to 120a^3.