Answer:
C. 2, 5, 15 and 45.
Step-by-step explanation:
Least common multiple (LCM)
The smallest multiple that two or more numbers have in common.
Find the prime factors of the given numbers:
- 2, 3 and 5 are prime numbers.
- Prime factorization of 15 = 3 × 5
- Prime factorization of 30 = 2 × 3 × 5
- Prime factorization of 45 = 3² × 5
To find the LCM of each set of given numbers, find the product of only those factors with the highest powers.
A: LCM of 2, 3, 15 and 30
List the prime factors of each number:
- 2 = 2
- 3 = 3
- 15 = 3 × 5
- 30 = 2 × 3 × 5
So the factors are 2, 3 and 5.
As the highest power of each factor is one, the LCM is 2 × 3 × 5 = 30.
B: LCM of 2, 5, 15 and 30
List the prime factors of each number:
- 2 = 2
- 5 = 5
- 15 = 3 × 5
- 30 = 2 × 3 × 5
So the factors are 2, 3 and 5.
As the highest power of each factor is one, the LCM is 2 × 3 × 5 = 30.
C: LCM of 2, 5, 15 and 45
List the prime factors of each number:
- 2 = 2
- 5 = 5
- 15 = 3 × 5
- 45 = 3² × 5
So the factors are 2, 3 and 5.
As the highest power of 2 and 5 is one, and the highest power of 3 is two, the LCM is 2 × 3² × 5 = 90.
D: LCM of 3, 5, 15 and 45
List the prime factors of each number:
- 3 = 3
- 5 = 5
- 15 = 3 × 5
- 45 = 3² × 5
So the factors are 3 and 5.
As the highest power of 3 is two, and the highest power of 5 is one, the LCM is 3² × 5 = 45.
