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Solution - Least common multiple (LCM) by prime factorization

33,880
33,880

Step-by-step explanation

1. Find the prime factors of 56

Tree view of the prime factors of 56: 2, 2, 2 and 7

The prime factors of 56 are 2, 2, 2 and 7.

2. Find the prime factors of 20

Tree view of the prime factors of 20: 2, 2 and 5

The prime factors of 20 are 2, 2 and 5.

3. 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.

4. Find the prime factors of 605

Tree view of the prime factors of 605: 5, 11 and 11

The prime factors of 605 are 5, 11 and 11.

5. Build a prime factors table

Determine the maximum number of times each prime factor (2, 5, 7, 11) occurs in the factorization of the given numbers:

Prime factorNumber56 20 44 605 Max. occurrence
232203
501011
710001
1100122

The prime factors 5 and 7 occur one time, while 2 and 11 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 = 222571111

LCM = 2357112

LCM = 33,880

The least common multiple of 56, 20, 44 and 605 is 33,880.

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.