The LCM of four numbers is 48. Three of them are 6, 8, and 12. What can be the…

Answer: 16

Reasoning:

• Find LCM of 6, 8, and 12 by prime factors: 6 = 2 × 3, 8 = 2^3, 12 = 2^2 × 3. Take highest powers: 2^3 and 3 → LCM = 2^3 × 3 = 24.

• Target LCM is 48 = 2^4 × 3, so the fourth number must supply an extra factor of 2 (raise 2^3 to 2^4).

Check each candidate:

• 16: equals 2^4, so including 16 raises the LCM to 2^4 × 3 = 48. Works.

• 24: equals 2^3 × 3 and divides 48, but the LCM of 6, 8, 12, and 24 remains 24, not 48. Does not work.

• 18: does not divide 48 (48 ÷ 18 is not an integer) and would require a higher power of 3. Does not work.

• 20: introduces prime factor 5, which would force the LCM to be a multiple of 5 (greater than 48). Does not work.

Conclusion: The fourth number must be 16.