Solution - Least common multiple (LCM) by prime factorization
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Least common multiple (LCM) by prime factorizationStep-by-step explanation
1. Find the prime factors of 396,000
The prime factors of 396,000 are 2, 2, 2, 2, 2, 3, 3, 5, 5, 5 and 11.
2. Find the prime factors of 210,000
The prime factors of 210,000 are 2, 2, 2, 2, 3, 5, 5, 5, 5 and 7.
3. Build a prime factors table
Determine the maximum number of times each prime factor (2, 3, 5, 7, 11) occurs in the factorization of the given numbers:
| Prime factorNumber | 396,000 | 210,000 | Max. occurrence |
| 2 | 5 | 4 | 5 |
| 3 | 2 | 1 | 2 |
| 5 | 3 | 4 | 4 |
| 7 | 0 | 1 | 1 |
| 11 | 1 | 0 | 1 |
The prime factors 7 and 11 occur one time, while 2, 3 and 5 occur more than once.
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Please leave us feedback.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.