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Solution - Least common multiple (LCM) by prime factorization

38,088
38,088

Step-by-step explanation

1. Find the prime factors of 3,174

Tree view of the prime factors of 3,174: 2, 3, 23 and 23

The prime factors of 3,174 are 2, 3, 23 and 23.

2. Find the prime factors of 4,761

Tree view of the prime factors of 4,761: 3, 3, 23 and 23

The prime factors of 4,761 are 3, 3, 23 and 23.

3. Find the prime factors of 9,522

Tree view of the prime factors of 9,522: 2, 3, 3, 23 and 23

The prime factors of 9,522 are 2, 3, 3, 23 and 23.

4. Find the prime factors of 12,696

Tree view of the prime factors of 12,696: 2, 2, 2, 3, 23 and 23

The prime factors of 12,696 are 2, 2, 2, 3, 23 and 23.

5. Build a prime factors table

Determine the maximum number of times each prime factor (2, 3, 23) occurs in the factorization of the given numbers:

Prime factorNumber3,1744,7619,52212,696Max. occurrence
210133
312212
2322222

The prime factors 2, 3 and 23 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 = 222332323

LCM = 2332232

LCM = 38,088

The least common multiple of 3,174, 4,761, 9,522 and 12,696 is 38,088.

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.