Answer :
To find the Least Common Multiple (L.C.M.) of two numbers when their Highest Common Factor (H.C.F.) is given, we can use the relationship between the H.C.F., L.C.M., and the product of the numbers.
For two numbers, the relationship is:
[tex]\text{H.C.F.} \times \text{L.C.M.} = \text{Product of the two numbers}[/tex]
Given:
- [tex]\text{H.C.F.} = 7[/tex]
- The numbers are 35 and 49.
First, find the product of the two numbers:
[tex]35 \times 49 = 1715[/tex]
Next, substitute the values into the relationship:
[tex]7 \times \text{L.C.M.} = 1715[/tex]
To find the L.C.M., divide the product by the H.C.F.:
[tex]\text{L.C.M.} = \frac{1715}{7} = 245[/tex]
Thus, the Least Common Multiple of 35 and 49 is 245.
Therefore, the correct option is (C) 245.
