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Solution - Least common multiple (LCM) by prime factorization

976,143
976,143

Step-by-step explanation

1. Find the prime factors of 43

43 is a prime factor.

2. Find the prime factors of 21

Tree view of the prime factors of 21: 3 and 7

The prime factors of 21 are 3 and 7.

3. Find the prime factors of 47

47 is a prime factor.

4. Find the prime factors of 23

23 is a prime factor.

5. Build a prime factors table

Determine the maximum number of times each prime factor (3, 7, 23, 43, 47) occurs in the factorization of the given numbers:

Prime factorNumber43 21 47 23 Max. occurrence
301001
701001
2300011
4310001
4700101

The prime factors 3, 7, 23, 43 and 47 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 = 37234347

LCM = 976,143

The least common multiple of 43, 21, 47 and 23 is 976,143.

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.