The Lcm Of 25 And 15 - Explained And Solved

LCM of 15 and 25 How to Find LCM of 15, 25? from www.cuemath.com

What is LCM?

LCM stands for the Least Common Multiple, which is the smallest number that both given numbers can divide into evenly. For example, the LCM of 4 and 6 is 12 because 12 is the smallest number that 4 and 6 can both divide into evenly.

Factors of 25 and 15

In order to find the LCM of 25 and 15, we need to first list out the factors of both numbers. Factors are the numbers that can divide into a given number without leaving a remainder. The factors of 25 are: 1, 5, 25 The factors of 15 are: 1, 3, 5, 15

Finding the Common Factors

Next, we need to identify the common factors between the two lists. In this case, the only common factor between 25 and 15 is 5.

Multiplying the Common Factors

To find the LCM, we need to multiply the common factors together. In this case, the only common factor is 5, so we simply multiply 5 by itself. LCM of 25 and 15: 5 x 5 = 25 Therefore, the LCM of 25 and 15 is 25.

Why is 25 the LCM?

We can check our answer by confirming that 25 is the smallest number that both 25 and 15 can divide into evenly. 25 can be divided by 5 (5 x 5) and 15 can be divided by 5 (3 x 5). Therefore, 25 is the smallest number that both 25 and 15 can divide into evenly.

Using Prime Factorization

Another method to find the LCM is by using prime factorization. Prime factorization involves breaking down each number into its prime factors and then finding the LCM by multiplying the highest powers of each prime factor. The prime factors of 25 are: 5 x 5 The prime factors of 15 are: 3 x 5 To find the LCM, we need to multiply the highest powers of each prime factor: Highest power of 3: 3^1 Highest power of 5: 5^2 LCM of 25 and 15: 3^1 x 5^2 = 75 Therefore, the LCM of 25 and 15 is 75.

When to Use LCM

LCM is commonly used in math problems involving fractions. When adding or subtracting fractions with different denominators, the LCM of the denominators is needed in order to find a common denominator. For example, to add 1/4 and 1/6, we need to find the LCM of 4 and 6 (which is 12) and then convert the fractions to have a denominator of 12 before adding them together.

Conclusion

In conclusion, the LCM of 25 and 15 is 25. This can be found by listing out the factors, identifying the common factors, and multiplying them together. Alternatively, prime factorization can be used to find the LCM. LCM is a useful tool in math, especially when working with fractions.