Find the LCM of the Following Numbers in Which One Number is the Factor of Other: 520, 618, 1248, 945. What Do You Observe in the Result Obtained?

To find the least common multiple (LCM) of the given numbers 520, 618, 1248, and 945, we first need to understand a few points about LCM.

The LCM of a set of numbers is the smallest number that is a multiple of each of the given numbers. When one number is a factor of another, the LCM is actually the larger number.

Let’s break down the numbers:

• 520: The prime factorization is 2³ × 5 × 13.
• 618: The prime factorization is 2 × 3 × 103.
• 1248: The prime factorization is 2⁴ × 3 × 13.
• 945: The prime factorization is 3 × 5 × 7 × 9.

Now, we’ll find the LCM:

1. From 520, we take 2³, 5, and 13.
2. From 618, we take 2 (but it is already included), 3, and 103.
3. From 1248, we take 2⁴ (which is more than in 520), 3 (already counted), and 13 (already counted).
4. From 945, we take 3 (already counted), 5 (already counted), and add 7.

Now, combining these factors, we take the highest power of each prime number:

• 2⁴
• 3¹
• 5¹
• 7¹
• 13¹
• 103¹

Now we calculate the LCM:

LCM = 2⁴ × 3 × 5 × 7 × 13 × 103

= 16 × 3 × 5 × 7 × 13 × 103

= 1,049,040

Observation: In this case, one important observation is when a number is a factor of another number, the LCM tends to equal the greatest of the numbers involved. Therefore, if we choose the number that is the largest and a multiple of the smallest, that could lead us to conclude that the LCM is keeping the highest factor as the result. This is evident when we examine 1248 and 520, where 1248 contributes more power to our LCM while maintaining the initial factorization integrity.