Question

If lcm of first 100 natural numbers is k, then lcm of first 105 natural numbers will be

Answer 1

According to the question the LCM of first 100 natural numbers is N.

And we know that 101 is a prime number. So there is no scope of any common factors in between 101 and N. Therefore the LCM of 101 and N = 101N.

Now we know that 102 can be resolved to product of 2 and 51. Since both the factors are less than 100 so it is quite obvious that 102 divides N.

Once again 103 is a prime number which means no common factors. Now in the case of next two numbers that is 104 and 105 both of them can be resolved to some factors that are having value less than hundred which means they divides N.

Therefore the LCM of first 105 natural numbers = N x 101 x 103.

Hope it helps.