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Solution - Least common multiple (LCM) by prime factorization

390,625
390,625

Step-by-step explanation

1. Find the prime factors of 125

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

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

2. Find the prime factors of 390,625

Tree view of the prime factors of 390,625: 5, 5, 5, 5, 5, 5, 5 and 5

The prime factors of 390,625 are 5, 5, 5, 5, 5, 5, 5 and 5.

3. Build a prime factors table

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

Prime factorNumber125 390,625Max. occurrence
5388

The prime factor 5 occurs more than once.

4. Calculate the LCM

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

LCM = 55555555

LCM = 58

LCM = 390,625

The least common multiple of 125 and 390,625 is 390,625.

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.