Question

If the lcm of first 20 natural no.
is x then find the lcm of first 25 natural no.

Answer 1

This is a great investigation into numbers...I encourage you to start a systematic table, working out the LCM for:
1
1, 2
1, 2, 3
1, 2, 3, 4
Etc.

You may then see a pattern developing that will help you answer your question.

Answer 2

first we need all primes < 20
2,3,5,7,11,13,17,19
including the perfect squares:
2,2,2,2,3,3,5,7,11,13,17,19

all we need are the extra factors caused by
21, 22, 23, 24, and 25
21 --- 3*7 already included
22 ---- already included
23 --------- we will need that
24 -----already included
25 -----already included

So the LCM from 1-25 is 23x

To actually find x :
first we need all primes < 20
2,3,5,7,11,13,17,19
including the perfect squares factors gives us :
2,2,2,2,3,3,5,7,11,13,17,19

x = 2*2*2*2*3*3*5*7*11*13*17*19 =232792560

Answer 3

Reiny's answer requires another factor, 5.

23*5*x