Question

The least common multiple of 24, 28 and 45 is:

Answer 1

Answer: 2520

Step-by-step explanation:

Answer 2

Answer:

B

Step-by-step explanation:

Find all prime factors

prime factors of 24 are 2, 2, 2 and 3.

The prime factors of 28 are 2, 2 and 7.

The prime factors of 45 are 3, 3 and 5.

Determine the maximum number of times each prime factor (2, 3, 5, 7) occurs in the factorization of the given numbers:

Prime factorNumber 24 28 45 Max. occurrence

2 3 2 0 3

3 1 0 2 2

5 0 0 1 1

7 0 1 0 1

The prime factors 5 and 7 occur one time, while 2 and 3 occur more than once.

The least common multiple is the product of all factors in the greatest number of their occurrence.

LCM = 2*2*2*3*3*5*7

LCM = 2^3*3^2*5*7

LCM = 2520

The least common multiple of 24, 28 and 45 is 2520.