Question

what is the least common multiple of 32 and 48?
a 196
b 8
c 96
d 118

Explanation:

Step1: Prime factorize 32

$32 = 2^5$

Step2: Prime factorize 48

$48 = 2^4 \times 3^1$

Step3: Take max exponents of primes

For prime 2: $\max(5,4)=5$; For prime 3: $\max(0,1)=1$

Step4: Calculate LCM

$\text{LCM} = 2^5 \times 3^1 = 32 \times 3 = 96$

Answer:

C. 96