Question

The H.C.F and L.C.M. of two numbers are 12 and 336 respectively. If one of the numbers is 48, the other is:

• A. 56
• B. 84
• C. 168
• D. 96

Hint:

The relationship between the H.C.F., L.C.M., and the product of two numbers is very useful for finding unknowns: \[ \text{H.C.F.} \times \text{L.C.M.} = \text{Product of the two numbers}. \]

Answer 1

The Correct Option is B

Use the relationship between H.C.F., L.C.M., and the product of two numbers.
We know that: \[ \text{H.C.F.} \times \text{L.C.M.} = \text{Product of the two numbers} \] Let the two numbers be \( x \) and \( y \). Here, we are given: \[ \text{H.C.F.} = 12, \quad \text{L.C.M.} = 336, \quad x = 48 \] Using the formula: \[ 12 \times 336 = 48 \times y \] Simplifying: \[ 4032 = 48 \times y \quad \Rightarrow \quad y = \frac{4032}{48} = 84 \]