Least Common Multiple (LCM) of 167 and 180
The least common multiple (LCM) of 167 and 180 is 30060.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 167 and 180?
First, calculate the GCD of 167 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 180 = 0 remainder 167 |
| 2 | 180 ÷ 167 = 1 remainder 13 |
| 3 | 167 ÷ 13 = 12 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 54 | 5886 |
| 103 and 20 | 2060 |
| 69 and 100 | 6900 |
| 57 and 77 | 4389 |
| 75 and 103 | 7725 |