The LCM of 6, 9 and x is 72. Which of the given options can be a possible value of x?
Given:
LCM(6, 9, x) = 72
Solution:
First, find LCM(6, 9):
6 = 2 × 3
9 = 3²
LCM(6, 9) = 2 × 3² = 18
Now check each option by computing LCM(18, x) = 72:
Option A: x = 24
24 = 2³ × 3
LCM(18, 24) = LCM(2 × 3², 2³ × 3) = 2³ × 3² = 72
Option B: x = 12
12 = 2² × 3
LCM(18, 12) = 2² × 3² = 36
Option C: x = 36
36 = 2² × 3²
LCM(18, 36) = 2² × 3² = 36
Option D: x = 18
18 = 2 × 3²
LCM(18, 18) = 18
Thus, Option (A) is right answer.
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