### Kth number with only prime factors of 3, 5 and 7.

##### Fact:

- Kth Multiple of 3, 5 and 7 =
`3`

^{k}* 5^{k}* 7^{k}

**Solution:**

- Take 3 queues
- Queue-3 to hold 3 multiples
- Queue-5 to hold 5 multiples
- Queue-7 to hold 7 multiples

- Remove minimum value from all three queues
- If we removed from Q3 then
- add Q3 * – If we removed from Q5 then
- add Q5 * – If we removed from Q7 then
- add Q7 * – – We’ll not add to Q3 and Q5 because it will be duplicate

##### Algorithm:

- Take three queue namely Q3, Q5 and Q7
- Add 1 to Q3
- Iterate 1 to K
- Fetch minimum_value from all three Queues
- If minimum_value == Q3.peek() then
- Q3.removeMin()
- Add Q3

- If minimum_value == Q5.peek() then
- Q5.removeMin()
- Add Q5

- If minimum_value == Q7.peek() then
- Q7.removeMin()

- Add Q7 * – return minimum_value

Latest Source Code:

Github: KthMultipleNumberOfThreeFiveAndSeven.java

**Output:**

When k==1 then Multiple = 1 When k==2 then Multiple = 3 When k==3 then Multiple = 5 When k==4 then Multiple = 7 When k==5 then Multiple = 9 When k==6 then Multiple = 15 When k==7 then Multiple = 21 When k==8 then Multiple = 25