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Solution - Least common multiple (LCM) by prime factorization

76,038
76,038

Step-by-step explanation

1. Find the prime factors of 46

Tree view of the prime factors of 46: 2 and 23

The prime factors of 46 are 2 and 23.

2. Find the prime factors of 29

29 is a prime factor.

3. Find the prime factors of 19

19 is a prime factor.

4. Find the prime factors of 3

3 is a prime factor.

5. Build a prime factors table

Determine the maximum number of times each prime factor (2, 3, 19, 23, 29) occurs in the factorization of the given numbers:

Prime factorNumber46 29 19 3 Max. occurrence
210001
300011
1900101
2310001
2901001

The prime factors 2, 3, 19, 23 and 29 occur one time.

6. Calculate the LCM

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

LCM = 23192329

LCM = 76,038

The least common multiple of 46, 29, 19 and 3 is 76,038.

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.