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.
