Enter an equation or problem
Camera input is not recognized!

Solution - Least common multiple (LCM) by prime factorization

3,360
3,360

Step-by-step explanation

1. Find the prime factors of 28

Tree view of the prime factors of 28: 2, 2 and 7

The prime factors of 28 are 2, 2 and 7.

2. Find the prime factors of 70

Tree view of the prime factors of 70: 2, 5 and 7

The prime factors of 70 are 2, 5 and 7.

3. Find the prime factors of 120

Tree view of the prime factors of 120: 2, 2, 2, 3 and 5

The prime factors of 120 are 2, 2, 2, 3 and 5.

4. Find the prime factors of 160

Tree view of the prime factors of 160: 2, 2, 2, 2, 2 and 5

The prime factors of 160 are 2, 2, 2, 2, 2 and 5.

5. Build a prime factors table

Determine the maximum number of times each prime factor (2, 3, 5, 7) occurs in the factorization of the given numbers:

Prime factorNumber28 70 120 160 Max. occurrence
221355
300101
501111
711001

The prime factors 3, 5 and 7 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 = 22222357

LCM = 25357

LCM = 3,360

The least common multiple of 28, 70, 120 and 160 is 3,360.

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.