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Solution - Least common multiple (LCM) by prime factorization

6,000
6,000

Step-by-step explanation

1. Find the prime factors of 240

Tree view of the prime factors of 240: 2, 2, 2, 2, 3 and 5

The prime factors of 240 are 2, 2, 2, 2, 3 and 5.

2. Find the prime factors of 750

Tree view of the prime factors of 750: 2, 3, 5, 5 and 5

The prime factors of 750 are 2, 3, 5, 5 and 5.

3. Find the prime factors of 24

Tree view of the prime factors of 24: 2, 2, 2 and 3

The prime factors of 24 are 2, 2, 2 and 3.

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) occurs in the factorization of the given numbers:

Prime factorNumber240 750 24 10 Max. occurrence
241314
311101
513013

The prime factor 3 occurs 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 = 22223555

LCM = 24353

LCM = 6,000

The least common multiple of 240, 750, 24 and 10 is 6,000.

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.