LCM of 5a^3 and 60a^2
To find the least common multiple (LCM) of 5a^3 and 60a^2, we need to find the highest power of each variable that appears in either expression and multiply them together.
The prime factorization of 5a^3 is:
5 × (a × a × a)
The prime factorization of 60a^2 is:
(2 × 2 × 3 × 5) × (a × a)
To find the LCM, we need to take the highest powers of each factor. Looking at the factor "5", it appears in 5a^3 but not in 60a^2, so we include it. Looking at the factor "2", it appears in 60a^2 but not in 5a^3, so we include it. The factor "3" does not appear in 5a^3, so we include it. Finally, the powers of "a" are higher in 5a^3 compared to 60a^2, so we take the highest power, which is a^3.
Combining all the factors, the LCM of 5a^3 and 60a^2 is:
5 × 2 × 2 × 3 × a^3 = 60a^3
To find the LCM (Least Common Multiple) of two terms, we need to determine the highest power for each variable that appears in both terms and multiply them together.
In this case, the two terms are 5a^3 and 60a^2. Let's break down each term:
Term 1: 5a^3
- The coefficient is 5.
- The variable is 'a' raised to the power of 3.
Term 2: 60a^2
- The coefficient is 60.
- The variable is 'a' raised to the power of 2.
To find the LCM, we need to determine the highest power of 'a' that appears in both terms. In this case, the highest power of 'a' is 3 since it appears in the first term, while the second term has 'a' raised to the power of 2.
Now, we multiply the coefficients of the terms to find the LCM of the coefficients. In this case, the LCM of 5 and 60 is 60.
Finally, we multiply the LCM of the coefficients (60) by the highest power of the variable 'a' (3) to get the LCM of the two terms:
LCM = 60 * a^3
Therefore, the LCM of 5a^3 and 60a^2 is 60a^3.
clearly the LCM of 5 and 60 is 60
and the LCM of a^3 and a^2 is a^3, so ......
5a and 60a
Well, for finding the least common multiple (LCM) of 5a^3 and 60a^2, we can start by finding the LCM of the coefficients, which is 5 and 60. The LCM of 5 and 60 is 60, but since we have a variable 'a', we also need to consider the variable with the highest exponent, which is a^3. Therefore, the LCM of 5a^3 and 60a^2 is 60a^3.
You could say that the LCM of 5a^3 and 60a^2 is like trying to find a common ground between five circus elephants and 60 acrobats. Sure, they might have their differences, but when it comes to finding a place where they can all comfortably coexist, we choose the largest possible tent - or, in this case, the LCM of 60a^3!