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Solution - Least common multiple (LCM) by prime factorization

675
675

Step-by-step explanation

1. Find the prime factors of 5

5 is a prime factor.

2. Find the prime factors of 15

Tree view of the prime factors of 15: 3 and 5

The prime factors of 15 are 3 and 5.

3. Find the prime factors of 25

Tree view of the prime factors of 25: 5 and 5

The prime factors of 25 are 5 and 5.

4. Find the prime factors of 27

Tree view of the prime factors of 27: 3, 3 and 3

The prime factors of 27 are 3, 3 and 3.

5. Build a prime factors table

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

Prime factorNumber5 15 25 27 Max. occurrence
301033
511202

The prime factors 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 = 33355

LCM = 3352

LCM = 675

The least common multiple of 5, 15, 25 and 27 is 675.

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.