Enter an equation or problem
Camera input is not recognized!

Solution - Least common multiple (LCM) by prime factorization

9,945
9,945

Step-by-step explanation

1. Find the prime factors of 17

17 is a prime factor.

2. Find the prime factors of 9

Tree view of the prime factors of 9: 3 and 3

The prime factors of 9 are 3 and 3.

3. Find the prime factors of 5

5 is a prime factor.

4. Find the prime factors of 13

13 is a prime factor.

5. Build a prime factors table

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

Prime factorNumber17 9 5 13 Max. occurrence
302002
500101
1300011
1710001

The prime factors 5, 13 and 17 occur one time, while 3 occurs more than once.

6. Calculate the LCM

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

LCM = 3351317

LCM = 3251317

LCM = 9,945

The least common multiple of 17, 9, 5 and 13 is 9,945.

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.