Enter an equation or problem
Camera input is not recognized!

Solution - Least common multiple (LCM) by prime factorization

1,122
1,122

Step-by-step explanation

1. Find the prime factors of 17

17 is a prime factor.

2. Find the prime factors of 22

Tree view of the prime factors of 22: 2 and 11

The prime factors of 22 are 2 and 11.

3. Find the prime factors of 33

Tree view of the prime factors of 33: 3 and 11

The prime factors of 33 are 3 and 11.

4. Find the prime factors of 102

Tree view of the prime factors of 102: 2, 3 and 17

The prime factors of 102 are 2, 3 and 17.

5. Build a prime factors table

Determine the maximum number of times each prime factor (2, 3, 11, 17) occurs in the factorization of the given numbers:

Prime factorNumber17 22 33 102 Max. occurrence
201011
300111
1101101
1710011

The prime factors 2, 3, 11 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 = 231117

LCM = 1,122

The least common multiple of 17, 22, 33 and 102 is 1,122.

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.