Enter an equation or problem
Camera input is not recognized!

Solution - Least common multiple (LCM) by prime factorization

36,465
36,465

Step-by-step explanation

1. Find the prime factors of 11

11 is a prime factor.

2. Find the prime factors of 13

13 is a prime factor.

3. Find the prime factors of 15

Tree view of the prime factors of 15: 3 and 5

The prime factors of 15 are 3 and 5.

4. Find the prime factors of 17

17 is a prime factor.

5. Build a prime factors table

Determine the maximum number of times each prime factor (3, 5, 11, 13, 17) occurs in the factorization of the given numbers:

Prime factorNumber11 13 15 17 Max. occurrence
300101
500101
1110001
1301001
1700011

The prime factors 3, 5, 11, 13 and 17 occur one time.

6. Calculate the LCM

The least common multiple is the product of all factors in the greatest number of their occurrence.

LCM = 35111317

LCM = 36,465

The least common multiple of 11, 13, 15 and 17 is 36,465.

Why learn this

The least common multiple (LCM), sometimes called the lowest common multiple or least common divisor, is helpful for understanding the relationships between numbers. For example, if it takes Earth 365 days to orbit the sun and it takes Venus 225 days to orbit the sun and both are in perfect alignment at the time this scenario is given, how long will it take for Earth and Venus to align again? We can use LCM to determine that the answer would be 16,425 days.

LCM is also a very important part of many mathematical concepts that also have real-world applications. For example, we use LCMs when adding and subtracting fractions, which we use quite frequently.