Find the least common multiple:
2b^2 and 12c^3
2 is the only number which divides both terms.
To find the least common multiple (LCM) of two or more terms, you need to find the smallest multiple that is divisible by each term.
Let's break down each term:
Term 1: 2b^2
Term 2: 12c^3
First, let's find the prime factors of each term:
Term 1: 2b^2
- 2 is a prime number and has no powers.
- b^2 has a base of b and an exponent of 2.
Term 2: 12c^3
- 12 = 2 * 2 * 3
- c^3 has a base of c and an exponent of 3.
Now, we need to determine which prime factors and their respective powers occur the most times when comparing both terms:
Prime factor: 2
- In Term 1: 2^1
- In Term 2: 2^2
Prime factor: 3
- In Term 1: 3^0
- In Term 2: 3^1
Prime factor: b
- In Term 1: b^2
- In Term 2: b^0
Prime factor: c
- In Term 1: c^0
- In Term 2: c^3
Finally, we need to multiply the prime factors with their respective highest powers to find the LCM:
LCM = (2^2) * (3^1) * (b^2) * (c^3)
Simplifying further, we get:
LCM = 4b^2c^3
Therefore, the least common multiple of 2b^2 and 12c^3 is 4b^2c^3.