I have used Euclid's method to find the L.C.M for two numbers.
l.c.m=a*b/(gcd(a,b))
How can I do this without using this algorithm? I have an idea of first getting all factors of these two numbers and storing them in array. Then take 1 element from array 1 and search for it in array2, if it present there then remove it from there and make the result multiply by that num.
Is this OK?
Almost. What's the LCM of 4 and 8? Obviously 8 (23), but in your method you'd find 2. You need to keep track not just of all factors, but also how often they appear.