Copyright Ⓒ 2013-2026
tiger-algebra.com

☰
Tiger Algebra Calculator Formatting help
Select Language
Add to Home
Tiger Algebra Solver
Are you looking for...
Camera Icon
Enter an equation or problem
Camera Icon
Camera input is not recognized!

Solution - Least common multiple (LCM) by prime factorization

1,130,000
1,130,000
See steps

Other Ways to Solve

Least common multiple (LCM) by prime factorization

Step-by-step explanation

1. Find the prime factors of 10,000

Tree view of the prime factors of 10,000: 2, 2, 2, 2, 5, 5, 5 and 5

The prime factors of 10,000 are 2, 2, 2, 2, 5, 5, 5 and 5.

2. Find the prime factors of 2,000

Tree view of the prime factors of 2,000: 2, 2, 2, 2, 5, 5 and 5

The prime factors of 2,000 are 2, 2, 2, 2, 5, 5 and 5.

3. Find the prime factors of 2,260

Tree view of the prime factors of 2,260: 2, 2, 5 and 113

The prime factors of 2,260 are 2, 2, 5 and 113.

4. Find the prime factors of 50

Tree view of the prime factors of 50: 2, 5 and 5

The prime factors of 50 are 2, 5 and 5.

5. Find the prime factors of 20

Tree view of the prime factors of 20: 2, 2 and 5

The prime factors of 20 are 2, 2 and 5.

6. Build a prime factors table

Determine the maximum number of times each prime factor (2, 5, 113) occurs in the factorization of the given numbers:

Prime factorNumber10,0002,0002,26050 20 Max. occurrence
2442124
5431214
113001001

The prime factor 113 occurs one time, while 2 and 5 occur more than once.

7. Calculate the LCM

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

LCM = 2⋅2⋅2⋅2⋅5⋅5⋅5⋅5⋅113

LCM = 24⋅54⋅113

LCM = 1,130,000

The least common multiple of 10,000, 2,000, 2,260, 50 and 20 is 1,130,000.

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.

Latest Related Drills Solved