Least Common Multiple (LCM) of 109 and 180
The least common multiple (LCM) of 109 and 180 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 109 and 180?
First, calculate the GCD of 109 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 180 = 0 remainder 109 |
| 2 | 180 ÷ 109 = 1 remainder 71 |
| 3 | 109 ÷ 71 = 1 remainder 38 |
| 4 | 71 ÷ 38 = 1 remainder 33 |
| 5 | 38 ÷ 33 = 1 remainder 5 |
| 6 | 33 ÷ 5 = 6 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 118 | 826 |
| 196 and 67 | 13132 |
| 181 and 39 | 7059 |
| 163 and 188 | 30644 |
| 42 and 106 | 2226 |