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Solution - Least common multiple (LCM) by prime factorization

12,100
12,100
See steps

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Least common multiple (LCM) by prime factorization

Step-by-step explanation

1. Find the prime factors of 6,050

Tree view of the prime factors of 6,050: 2, 5, 5, 11 and 11

The prime factors of 6,050 are 2, 5, 5, 11 and 11.

2. Find the prime factors of 484

Tree view of the prime factors of 484: 2, 2, 11 and 11

The prime factors of 484 are 2, 2, 11 and 11.

3. Find the prime factors of 1,100

Tree view of the prime factors of 1,100: 2, 2, 5, 5 and 11

The prime factors of 1,100 are 2, 2, 5, 5 and 11.

4. Find the prime factors of 1,210

Tree view of the prime factors of 1,210: 2, 5, 11 and 11

The prime factors of 1,210 are 2, 5, 11 and 11.

5. Build a prime factors table

Determine the maximum number of times each prime factor (2, 5, 11) occurs in the factorization of the given numbers:

Prime factorNumber6,050484 1,1001,210Max. occurrence
212212
520212
1122122

The prime factors 2, 5 and 11 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⋅5⋅5⋅11⋅11

LCM = 22⋅52⋅112

LCM = 12,100

The least common multiple of 6,050, 484, 1,100 and 1,210 is 12,100.

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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