Question

If x is the LCM of 4, 6, 8 and y is the LCM of 3, 5, 7 and p is the LCM of x and y, then which of the following is true? 

Options

• p = 35x

• p = 4y

• p = 8x

• p = 16y

Answer 1

p = 35x

Explanation:

• Step 1: Find x (LCM of 4, 6, and 8)
  Prime factorisations:
  • 4 = 2²
  • 6 = 2 × 3
  • 8 = 2³
• LCM is obtained by taking the highest powers of all prime factors:
  • LCM(4, 6, 8) = 2³ × 3 = 24
  • So, x = 24
• Step 2: Find y (LCM of 3, 5, and 7)
  Prime factorisations:
  
  • 3 = 3
  • 5 = 5
  • 7 = 7
• Since all are distinct primes, their LCM is simply their product:
  • LCM(3, 5, 7) = 3 × 5 × 7 = 105
  • So, y = 105.
• Step 3: Find p (LCM of x and y):
  
  • x = 24, y = 105
  • Prime factorisation:
    • 24 = 2³ × 3
    • 105 = 3 × 5 × 7
  • LCM(24, 105) takes the highest powers of all prime factors:
    • LCM(24, 105) = 2³ × 3 × 5 × 7 = 840
    • So, p = 840

p = 35x

840 = 35 × 24

840 = 840