Question : The LCM of 96, 132, and 438 is:
Option 1: 86084
Option 2: 67055
Option 3: 85046
Option 4: 77088
Correct Answer: 77088
Solution :
The prime factorization of the given numbers is:
$96 = 2^5 \times 3 $
$132 = 2^2 \times 3^1 \times 11^1 \\$
$438 = 2^1 \times 3^1 \times 73^1$
Now, identify the highest powers of each prime factor:
It is $2^5$,$3^1$,$11^1$, and $73^1$
Multiply these highest powers to find the LCM:
$\text{LCM of}\;(96, 132, 438) = 2^5 \times 3^1 \times 11^1 \times 73^1 = 77088$
Hence, the correct answer is 77088.
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