Question

The G.C.D. and L.C.M of two numbers are 12 and 252 respectively. If one number is 36, then the other number is

• A. 44
• B. 32
• C. 26
• D. 84

Hint:

Use the relation \( \text{G.C.D.}(a, b) \times \text{L.C.M.}(a, b) = a \times b \) to find the missing number when one number is known.

Answer 1

The Correct Option is D

We know that the product of the G.C.D. and L.C.M. of two numbers is equal to the product of the numbers themselves. Let the two numbers be \( a \) and \( b \), and we are given: \[ \text{G.C.D.}(a, b) = 12, \quad \text{L.C.M.}(a, b) = 252, \quad a = 36. \] Then, we can use the relation: \[ \text{G.C.D.}(a, b) \times \text{L.C.M.}(a, b) = a \times b. \] Substitute the known values: \[ 12 \times 252 = 36 \times b \quad \Rightarrow \quad 3024 = 36 \times b \quad \Rightarrow \quad b = \frac{3024}{36} = 84. \]