Solution - Least common multiple (LCM) by prime factorization

Solution - Least common multiple (LCM) by prime factorization

Solution - Least common multiple (LCM) by prime factorization

Step-by-step explanation

Why learn this

Step-by-step explanation

Why learn this

Terms and topics

Related links

Step-by-step explanation

Why learn this

Terms and topics

Related links

1. Find the prime factors of 1

2. Find the prime factors of 8

3. Find the prime factors of 27

4. Find the prime factors of 64

5. Find the prime factors of 125

6. Build a prime factors table

7. Calculate the LCM

1. Find the prime factors of 1

2. Find the prime factors of 8

3. Find the prime factors of 27

4. Find the prime factors of 64

5. Find the prime factors of 125

6. Build a prime factors table

7. Calculate the LCM

1. Find the prime factors of 1

2. Find the prime factors of 8

3. Find the prime factors of 27

4. Find the prime factors of 64

5. Find the prime factors of 125

6. Build a prime factors table

7. Calculate the LCM

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216, 000

216,000

See steps

1 is a prime factor.

Tree view of the prime factors of 8: 2, 2 and 2

The prime factors of 8 are 2, 2 and 2.

Tree view of the prime factors of 27: 3, 3 and 3

The prime factors of 27 are 3, 3 and 3.

Tree view of the prime factors of 64: 2, 2, 2, 2, 2 and 2

The prime factors of 64 are 2, 2, 2, 2, 2 and 2.

Tree view of the prime factors of 125: 5, 5 and 5

The prime factors of 125 are 5, 5 and 5.

Determine the maximum number of times each prime factor (1, 2, 3, 5) occurs in the factorization of the given numbers:

The prime factor 1 occurs one time, while 2, 3 and 5 occur more than once.

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

LCM = $1 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 5 \cdot 5 \cdot 5$

LCM = $1 \cdot 2^{6} \cdot 3^{3} \cdot 5^{3}$

LCM = 216,000

The least common multiple of 1, 8, 27, 64 and 125 is 216,000.

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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.

Prime factorNumber

Max. occurrence