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

1,000
1,000
See steps

Other Ways to Solve

Least common multiple (LCM) by prime factorization

Step-by-step explanation

1. Find the prime factors of 100

Tree view of the prime factors of 100: 2, 2, 5 and 5

The prime factors of 100 are 2, 2, 5 and 5.

2. Find the prime factors of 200

Tree view of the prime factors of 200: 2, 2, 2, 5 and 5

The prime factors of 200 are 2, 2, 2, 5 and 5.

3. Find the prime factors of 250

Tree view of the prime factors of 250: 2, 5, 5 and 5

The prime factors of 250 are 2, 5, 5 and 5.

4. Find the prime factors of 500

Tree view of the prime factors of 500: 2, 2, 5, 5 and 5

The prime factors of 500 are 2, 2, 5, 5 and 5.

5. Build a prime factors table

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

Prime factorNumber100 200 250 500 Max. occurrence
223123
522333

The prime factors 2 and 5 occur 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 = 2⋅2⋅2⋅5⋅5⋅5

LCM = 23⋅53

LCM = 1,000

The least common multiple of 100, 200, 250 and 500 is 1,000.

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