Enter an equation or problem
Camera input is not recognized!

Solution - Least common multiple (LCM) by prime factorization

24,480
24,480

Step-by-step explanation

1. Find the prime factors of 60

Tree view of the prime factors of 60: 2, 2, 3 and 5

The prime factors of 60 are 2, 2, 3 and 5.

2. Find the prime factors of 72

Tree view of the prime factors of 72: 2, 2, 2, 3 and 3

The prime factors of 72 are 2, 2, 2, 3 and 3.

3. Find the prime factors of 85

Tree view of the prime factors of 85: 5 and 17

The prime factors of 85 are 5 and 17.

4. Find the prime factors of 96

Tree view of the prime factors of 96: 2, 2, 2, 2, 2 and 3

The prime factors of 96 are 2, 2, 2, 2, 2 and 3.

5. Build a prime factors table

Determine the maximum number of times each prime factor (2, 3, 5, 17) occurs in the factorization of the given numbers:

Prime factorNumber60 72 85 96 Max. occurrence
223055
312012
510101
1700101

The prime factors 5 and 17 occur one time, while 2 and 3 occur 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 = 2222233517

LCM = 2532517

LCM = 24,480

The least common multiple of 60, 72, 85 and 96 is 24,480.

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.