Least Common Multiple (LCM) of 180 and 187
The least common multiple (LCM) of 180 and 187 is 33660.
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 187?
First, calculate the GCD of 180 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 187 = 0 remainder 180 |
| 2 | 187 ÷ 180 = 1 remainder 7 |
| 3 | 180 ÷ 7 = 25 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 89 | 1424 |
| 125 and 137 | 17125 |
| 130 and 83 | 10790 |
| 72 and 172 | 3096 |
| 97 and 163 | 15811 |