What are all the LCM (least common multiples) of 15, 20 and 25?

To find the least common multiples (LCM) of the numbers 15, 20, and 25, we can follow a systematic approach.

Step 1: Prime Factorization

First, we need to break down each number into its prime factors:

• 15: 3 × 5
• 20: 2² × 5
• 25: 5²

Step 2: Identify the Highest Powers

Next, we take the highest power of each prime factor present in the factorizations:

• For 2: 2² (from 20)
• For 3: 3¹ (from 15)
• For 5: 5² (from 25)

Step 3: Calculate the LCM

Now, we multiply these highest powers together to find the LCM:

LCM = 2² × 3¹ × 5²

Calculating this gives:

• 2² = 4
• 3¹ = 3
• 5² = 25

Now, multiply these results:

4 × 3 = 12

12 × 25 = 300

Final Result

The least common multiple of 15, 20, and 25 is 300.