Prime Factorization of 105 and 106
Prime Factorization of 105 and 106

Least common multiple (LCM) by prime factorization

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lcm(105,225)

This solution deals with the least common multiple (LCM) by prime factorization.

Step-by-step explanation

  • Least common multiple (LCM) by prime factorization

3. Build a prime factors table

Determine the maximum number of times each prime factor (3, 5, 7) occurs in the factorization of the given numbers:

Prime factorNumber 105 225 Max. occurrence
3 1 2 2
5 1 2 2
7 1 0 1

The prime factor 7 occurs one time, while 3 and 5 occur more than once.

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.

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