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Solution - Least common multiple (LCM) by prime factorization

35,937
35,937

Step-by-step explanation

1. Find the prime factors of 33

Tree view of the prime factors of 33: 3 and 11

The prime factors of 33 are 3 and 11.

2. 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.

3. Find the prime factors of 121

Tree view of the prime factors of 121: 11 and 11

The prime factors of 121 are 11 and 11.

4. Find the prime factors of 1,331

Tree view of the prime factors of 1,331: 11, 11 and 11

The prime factors of 1,331 are 11, 11 and 11.

5. Find the prime factors of 1,089

Tree view of the prime factors of 1,089: 3, 3, 11 and 11

The prime factors of 1,089 are 3, 3, 11 and 11.

6. Build a prime factors table

Determine the maximum number of times each prime factor (3, 11) occurs in the factorization of the given numbers:

Prime factorNumber33 27 121 1,3311,089Max. occurrence
3130023
11102323

The prime factors 3 and 11 occur more than once.

7. Calculate the LCM

The least common multiple is the product of all factors in the greatest number of their occurrence.

LCM = 333111111

LCM = 33113

LCM = 35,937

The least common multiple of 33, 27, 121, 1,331 and 1,089 is 35,937.

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.