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Solution - Least common multiple (LCM) by prime factorization

396
396

Step-by-step explanation

1. Find the prime factors of 22

Tree view of the prime factors of 22: 2 and 11

The prime factors of 22 are 2 and 11.

2. Find the prime factors of 44

Tree view of the prime factors of 44: 2, 2 and 11

The prime factors of 44 are 2, 2 and 11.

3. Find the prime factors of 66

Tree view of the prime factors of 66: 2, 3 and 11

The prime factors of 66 are 2, 3 and 11.

4. Find the prime factors of 99

Tree view of the prime factors of 99: 3, 3 and 11

The prime factors of 99 are 3, 3 and 11.

5. Build a prime factors table

Determine the maximum number of times each prime factor (2, 3, 11) occurs in the factorization of the given numbers:

Prime factorNumber22 44 66 99 Max. occurrence
212102
300122
1111111

The prime factor 11 occurs one time, while 2 and 3 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 = 223311

LCM = 223211

LCM = 396

The least common multiple of 22, 44, 66 and 99 is 396.

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.