Least Common Multiple (LCM) of 180 and 167
The least common multiple (LCM) of 180 and 167 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 180 and 167?
First, calculate the GCD of 180 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 167 = 1 remainder 13 |
| 2 | 167 ÷ 13 = 12 remainder 11 |
| 3 | 13 ÷ 11 = 1 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 51 | 663 |
| 169 and 88 | 14872 |
| 194 and 168 | 16296 |
| 21 and 97 | 2037 |
| 94 and 83 | 7802 |