Question

Find the minimum positive integer that can be divisible by 2 to 10 integers.​

Answer 1

Answer: 2520

We have the following numbers that should divide the least positive integer. Which are:

• 2, 3, 4, 5, 6, 7, 8, 9, 10

Finding a number which is divisible by all these numbers is simple, Just multiply all the numbers.

But, We should remember LCM (Least common multiple) that LCM of numbers is the number that is divisible by those numbers.

Hence, We should find the LCM of all these numbers to get our answer.

So, Let's find the prime factorisation of these numbers:

• 2 = 1 × 2
• 3 = 1 × 3
• 4 = 2 × 2 = 2²
• 5 = 5 × 1
• 6 = 3 × 2
• 7 = 7 × 1
• 8 = 2 × 2 × 2
• 9 = 3 × 3
• 10 = 5 × 2

Now, we know, LCM of numbers is given by:

⇒ LCM = Product of prime factors with highest power

We can see that,

• Highest power of 2 is in prime factorisation of 8 which is 3.
• Highest power of 4 is in prime factorisation of 9 which is 2.

All the other factors have the highest power 1, So

⇒ LCM = 2³ × 3² × 5 × 7

⇒ LCM = 8 × 9 × 5 × 7

⇒ LCM = 2520

Hence, The least positive integer which is divisible by the numbers from 2 to 10 is 2520.

Answer 2

Step-by-step explanation:

Answer:✍️

2520

We have the following numbers that should divide the least positive integer. Which are:

2, 3, 4, 5, 6, 7, 8, 9, 10

Finding a number which is divisible by all these numbers is simple, Just multiply all the numbers.

But, We should remember LCM (Least common multiple) that LCM of numbers is the number that is divisible by those numbers.

Hence, We should find the LCM of all these numbers to get our answer.

So, Let's find the prime factorisation of these numbers:

2 = 1 × 2

3 = 1 × 3

4 = 2 × 2 = 2²

5 = 5 × 1

6 = 3 × 2

7 = 7 × 1

8 = 2 × 2 × 2

9 = 3 × 3

10 = 5 × 2

Now, we know, LCM of numbers is given by:

⇒ LCM = Product of prime factors with highest power

We can see that,

Highest power of 2 is in prime factorisation of 8 which is 3.

Highest power of 4 is in prime factorisation of 9 which is 2.

All the other factors have the highest power 1, So

⇒ LCM = 2³ × 3² × 5 × 7

⇒ LCM = 8 × 9 × 5 × 7

⇒ LCM = 2520

Hence, The least positive integer which is divisible by the numbers from 2 to 10 is 2520.

hope this helps you!!

thank you ⭐