The LCM of 48, 88 and another number, x, is 4752. Which of the following can be the value of x?

Correct option is C

Given:

LCM of 48, 88, x = 4752

We are to find which of the given options could be a possible value of x 

Solution:

Prime factorizations:

48 = $$2^4 \times 3$$​​

88 = $$2^3 \times11$$​​

LCM(48, 88) = $$2^4\times 3 \times 11$$ = 528

Now,

LCM(48, 88, x) = 4752

From the option;

Option A: 202

202 = 2 × 101

LCM(528, 202) will include 101 → LCM becomes too large (>4752) 

Option B: 307

307 is prime → LCM(528, 307) = 528 × 307 = 162096 

Option C: 216

216 = 2³ × 3³

LCM(528, 216) = 2⁴ × 3³ × 11 = 16 × 27 × 11 = 4752 

Option D: 123

123 = 3 × 41 → LCM(528, 123) = includes 41 → becomes 21648  
Hence Option (c) is the correct answer.