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Solution - Least common multiple (LCM) by prime factorization

1,800
1,800
See steps

Other Ways to Solve

Least common multiple (LCM) by prime factorization

Step-by-step explanation

1. 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.

2. Find the prime factors of 300

Tree view of the prime factors of 300: 2, 2, 3, 5 and 5

The prime factors of 300 are 2, 2, 3, 5 and 5.

3. Find the prime factors of 360

Tree view of the prime factors of 360: 2, 2, 2, 3, 3 and 5

The prime factors of 360 are 2, 2, 2, 3, 3 and 5.

4. Find the prime factors of 450

Tree view of the prime factors of 450: 2, 3, 3, 5 and 5

The prime factors of 450 are 2, 3, 3, 5 and 5.

5. Build a prime factors table

Determine the maximum number of times each prime factor (2, 3, 5) occurs in the factorization of the given numbers:

Prime factorNumber200 300 360 450 Max. occurrence
232313
301222
522122

The prime factors 2, 3 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⋅3⋅3⋅5⋅5

LCM = 23⋅32⋅52

LCM = 1,800

The least common multiple of 200, 300, 360 and 450 is 1,800.

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.

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