Least common multiple of the monomial 5a^2 and 16a^3
LCM of the monomials 5a^2 and 16a^2 is 80a^2.
5a^2 --- 5 x a^2
16^2 --- 2^4 x a^2
a^2 and a^2 cancel out to a^2
2^4 x 5 x a^2 = 16 x 5 x a^2 = 80a^2
LCM of 5 and 16 is 80
LCM of a^2 and a^3, so you want 80a^3
My bad--- 80a^3--- i thought they were both a^2
Idk to the 3rd power
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To find the least common multiple (LCM) of the monomials 5a^2 and 16a^3, we need to determine the smallest expression that is divisible by both terms.
First, let's break down each monomial into its prime factors:
5a^2 can be written as 5 * a * a.
16a^3 can be written as 2 * 2 * 2 * 2 * a * a * a.
Next, we identify the highest power of each prime factor that appears in either monomial:
5a^2: prime factor "5" appears once, and "a" appears twice.
16a^3: prime factor "2" appears four times, and "a" appears three times.
Now, we take the highest power of each prime factor that appears in either monomial:
- Prime factor "5" appears once in 5a^2 and zero times in 16a^3.
- Prime factor "2" appears four times in 16a^3 and zero times in 5a^2.
- Prime factor "a" appears three times in 16a^3 and twice in 5a^2.
Finally, we multiply the prime factors together with their highest powers to get the LCM:
5 * 2^4 * a^3 = 80a^3
Therefore, the least common multiple of the monomials 5a^2 and 16a^3 is 80a^3.