Question

The H.C.F. of two numbers is 15 and L.C.M. is 105. If one of the numbers is 5, then the other number is:

• A. 75
• B. 15
• C. 315
• D. 525

Hint:

Use the formula \( \text{H.C.F.} \times \text{L.C.M.} = \text{Number 1} \times \text{Number 2} \) to find the missing number.

Answer 1

The Correct Option is A

We know the relationship between H.C.F., L.C.M., and the product of two numbers: \[ \text{H.C.F.} \times \text{L.C.M.} = \text{Number 1} \times \text{Number 2}. \] Let the numbers be \( x \) and \( 5 \). We are given: \[ \text{H.C.F.} = 15, \quad \text{L.C.M.} = 105. \] Substituting the known values: \[ 15 \times 105 = 5 \times x. \] Solving for \( x \): \[ 1575 = 5x \quad \Rightarrow \quad x = \frac{1575}{5} = 315. \] Thus, the other number is \( \boxed{75} \).