Understanding Lcm For 6 And 15

LCM of 6 and 15 How to Find LCM of 6, 15? from www.cuemath.com

What is LCM?

LCM stands for Least Common Multiple. It is the smallest number that can be divided by both of the given numbers without any remainder. In simpler terms, it is the smallest number that both numbers can go into evenly.

How to Find LCM?

To find the LCM of two numbers, we can use the prime factorization method. We break down the numbers into their prime factors and then multiply the common factors together. If there are any remaining factors that are not common, we multiply them as well.

Prime Factorization of 6

To find the prime factors of 6, we start by dividing it by the smallest prime number, which is 2. We get 3 as the quotient, but since 3 is a prime number, we stop here. Therefore, the prime factors of 6 are 2 and 3.

Prime Factorization of 15

To find the prime factors of 15, we start by dividing it by 3, which is the smallest prime factor. We get 5 as the quotient, which is also a prime number. Therefore, the prime factors of 15 are 3 and 5.

Finding LCM of 6 and 15

To find the LCM of 6 and 15, we first write down their prime factorization: 6 = 2 x 3 15 = 3 x 5 We can see that both numbers have a common factor of 3. Therefore, we multiply 3 once and remove it from both numbers: 6 = 2 x 3 15 = 5 Now, we multiply the remaining factors together: 2 x 3 x 5 = 30 Therefore, the LCM of 6 and 15 is 30.

Why is LCM Important?

LCM is an important concept in mathematics and is used in many real-life situations. It is used in calculations involving fractions, ratios, and proportions. LCM is also used in finding the period of time when two events occur at different intervals.

Conclusion

In conclusion, the LCM of 6 and 15 is 30, which is the smallest number that both 6 and 15 can go into evenly. LCM is an important concept in mathematics and is used in various calculations. By understanding how to find LCM, we can solve many mathematical problems with ease.