Find the least common multiple of 15 and 25
To find the least common multiple (LCM) of 15 and 25, we can list the multiples of each number and find the smallest number that appears in both lists.
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ...
Multiples of 25: 25, 50, 75, 100, 125, 150, ...
From the lists above, we can see that the least common multiple of 15 and 25 is 75.
To find the least common multiple (LCM) of two numbers, we can use the prime factorization method.
Step 1: Prime Factorization
Let's find the prime factorization of both 15 and 25.
15: 15 can be broken down into prime factors as 3 * 5
25: 25 can be expressed as 5 * 5
Step 2: LCM Calculation
The LCM is the product of the highest powers of all the prime factors in the given numbers.
From the prime factorization of 15, we have 3 * 5.
From the prime factorization of 25, we have 5 * 5.
Note that both 3 and 5 are prime numbers.
To calculate the LCM, we take the highest power of 3, which is 1, and the highest power of 5, which is 2.
LCM = 3^1 * 5^2
= 3 * 25
= 75
Therefore, the least common multiple of 15 and 25 is 75.
To find the least common multiple (LCM) of two numbers, you can follow these steps:
Step 1: Write down the prime factorization of each number.
15 = 3 x 5
25 = 5 x 5
Step 2: Identify the highest power of each prime factor that appears in either factorization.
The only prime number in common between 15 and 25 is 5. The highest power is 5^2.
Step 3: Multiply all the prime factors from both numbers, using the highest power of each.
LCM = 3 x 5^2 = 3 x 25 = 75
Therefore, the least common multiple of 15 and 25 is 75.