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Solution - Least common multiple (LCM) by prime factorization

32,400
32,400

Step-by-step explanation

1. Find the prime factors of 10

Tree view of the prime factors of 10: 2 and 5

The prime factors of 10 are 2 and 5.

2. Find the prime factors of 16

Tree view of the prime factors of 16: 2, 2, 2 and 2

The prime factors of 16 are 2, 2, 2 and 2.

3. Find the prime factors of 81

Tree view of the prime factors of 81: 3, 3, 3 and 3

The prime factors of 81 are 3, 3, 3 and 3.

4. Find the prime factors of 900

Tree view of the prime factors of 900: 2, 2, 3, 3, 5 and 5

The prime factors of 900 are 2, 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 factorNumber10 16 81 900 Max. occurrence
214024
300424
510022

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 = 2222333355

LCM = 243452

LCM = 32,400

The least common multiple of 10, 16, 81 and 900 is 32,400.

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.