Enter an equation or problem
Camera input is not recognized!

Solution - Least common multiple (LCM) by prime factorization

348
348

Step-by-step explanation

1. Find the prime factors of 58

Tree view of the prime factors of 58: 2 and 29

The prime factors of 58 are 2 and 29.

2. Find the prime factors of 87

Tree view of the prime factors of 87: 3 and 29

The prime factors of 87 are 3 and 29.

3. Find the prime factors of 116

Tree view of the prime factors of 116: 2, 2 and 29

The prime factors of 116 are 2, 2 and 29.

4. Find the prime factors of 174

Tree view of the prime factors of 174: 2, 3 and 29

The prime factors of 174 are 2, 3 and 29.

5. Build a prime factors table

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

Prime factorNumber58 87 116 174 Max. occurrence
210212
301011
2911111

The prime factors 3 and 29 occur one time, while 2 occurs more than once.

6. Calculate the LCM

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

LCM = 22329

LCM = 22329

LCM = 348

The least common multiple of 58, 87, 116 and 174 is 348.

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.