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Solution - Least common multiple (LCM) by prime factorization

4,290
4,290

Step-by-step explanation

1. Find the prime factors of 13

13 is a prime factor.

2. Find the prime factors of 11

11 is a prime factor.

3. 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.

4. 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.

5. Build a prime factors table

Determine the maximum number of times each prime factor (2, 3, 5, 11, 13) occurs in the factorization of the given numbers:

Prime factorNumber13 11 15 10 Max. occurrence
200011
300101
500111
1101001
1310001

The prime factors 2, 3, 5, 11 and 13 occur one time.

6. Calculate the LCM

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

LCM = 2351113

LCM = 4,290

The least common multiple of 13, 11, 15 and 10 is 4,290.

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.