Least Common Multiple (LCM) of 180 and 109
The least common multiple (LCM) of 180 and 109 is 19620.
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 109?
First, calculate the GCD of 180 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 109 = 1 remainder 71 |
| 2 | 109 ÷ 71 = 1 remainder 38 |
| 3 | 71 ÷ 38 = 1 remainder 33 |
| 4 | 38 ÷ 33 = 1 remainder 5 |
| 5 | 33 ÷ 5 = 6 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 108 | 2160 |
| 29 and 197 | 5713 |
| 189 and 107 | 20223 |
| 109 and 114 | 12426 |
| 67 and 119 | 7973 |