The LCM (Least Common Multiple) of two numbers is the smallest number that is a multiple of both.

Step 1: Identify the numbers. Here, the numbers are p and (p + 1).

Step 2: Understand that a prime number is a number that has only two distinct positive divisors: 1 and itself. So, p is a prime number.

Step 3: The LCM of two consecutive numbers is always the product of the two numbers. This is because two consecutive numbers are always co-prime, i.e., their greatest common divisor (GCD) is 1.

Step 4: Therefore, the LCM of p and (p + 1) is p*(p + 1).

Question

The LCM (Least Common Multiple) of two numbers is the smallest number that is a multiple of both.

Step 1: Identify the numbers. Here, the numbers are p and (p + 1).

Step 2: Understand that a prime number is a number that has only two distinct positive divisors: 1 and itself. So, p is a prime number.

Step 3: The LCM of two consecutive numbers is always the product of the two numbers. This is because two consecutive numbers are always co-prime, i.e., their greatest common divisor (GCD) is 1.

Step 4: Therefore, the LCM of p and (p + 1) is p*(p + 1).

Knowee AI · Accepted Answer

The LCM (Least Common Multiple) of two numbers is the smallest number that is a multiple of both.

Step 1: Identify the numbers. Here, the numbers are p and (p + 1).

Step 2: Understand that a prime number is a number that has only two distinct positive divisors: 1 and itself. So, p is a prime number.

Step 3: The LCM of two consecutive numbers is always the product of the two numbers. This is because two consecutive numbers are always co-prime, i.e., their greatest common divisor (GCD) is 1.

Step 4: Therefore, the LCM of p and (p + 1) is p*(p + 1).

If p is a prime number, then the LCM of p and (p + 1) :

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