multiply two dataframes by matching rows and columns

I would like to multiply two data frames or matrices by matching the rows in Df1 with column names in DF2. The data frames look like

Df1<- 
| ID   |Value|
|:---- |:----|
| 105  |213|
| 105  |214|
| 90  |215|
| 90  |216|
| 100  |217|

Df2<- 
| 90 | 100 | 105 |
|:---- |:------:| -----:|
| 10 | 11    | 12 |
| 15  | 20    | 25 |
| 20  | 25    | 30 |

My goal is to match the 'ID' in Df1 with the colnames in Df2 and multiply the Value in Df1 with the matched columns in the Df2. The output should look like:

output<-

What would be the fastest and convenient method to do this. I am relatively new to the R and any help is highly appreciated.

Update

We can try

with(
  df1,
  as.data.frame(t(t(unname(df2[as.character(ID)])) * Value))
)

which gives

    V1   V2   V3   V4   V5
1 2556 2568 2150 2160 2387
2 5325 5350 3225 3240 4340
3 6390 6420 4300 4320 5425

Maybe this base R code with reshape + merge could help

reshape(
  transform(
    type.convert(
      merge(df1, stack(df2), by.x = "ID", by.y = "ind", all = TRUE),
      as.is = TRUE
    ),
    idx = ave(ID, ID, Value, FUN = seq_along),
    p = Value * values
  )[c("Value", "idx", "p")],
  direction = "wide",
  idvar = "idx",
  timevar = "Value"
)

which gives

  idx p.215 p.216 p.217 p.213 p.214
1   1  3225  3240  5425  6390  6420
2   2  2150  2160  2387  2556  2568
3   3  4300  4320  4340  5325  5350

Data

df1 <- data.frame(
  ID = c(105, 105, 90, 90, 100),
  Value = 213:217
)

df2 <- data.frame(
  `90` = c(10, 15, 20),
  `100` = c(11, 20, 25),
  `105` = c(12, 25, 30),
  check.names = FALSE
)