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Solution - Least common multiple (LCM) by prime factorization

13,200
13,200

Step-by-step explanation

1. Find the prime factors of 11

11 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 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.

4. 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.

5. Build a prime factors table

Determine the maximum number of times each prime factor (2, 3, 5, 11) occurs in the factorization of the given numbers:

Prime factorNumber11 15 16 25 Max. occurrence
200404
301001
501022
1110001

The prime factors 3 and 11 occur one time, while 2 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 = 222235511

LCM = 2435211

LCM = 13,200

The least common multiple of 11, 15, 16 and 25 is 13,200.

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.