Question

The lcm of first 70 natural numbers is N. The lcm of first 75 natural numbers is

Answer 1

Given:

The lcm of first 70 natural numbers is N.

To find:

The lcm of first 75 natural numbers

Solution:

From given, we have,

The lcm of first 70 natural numbers is N.

Now 71 is prime number, Hence the lcm becomes

LCM = 71 × N

72 = 36 × 2 Therefore, 72 divides N

Now 73 is prime number, Hence the lcm becomes

LCM = 71 × N × 73

74 = 37 × 2 Therefore, 74 divides N

75 = 15 × 5 Therefore, 75 divides N

Hence the lcm of first 75 natural numbers is 71 × N × 73

Answer 2

Step-by-step explanation:

hence lcm will be 5183 N as explained in the above picture