Least Common Multiple (LCM) of 109 and 186
The least common multiple (LCM) of 109 and 186 is 20274.
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 186?
First, calculate the GCD of 109 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 186 = 0 remainder 109 |
| 2 | 186 ÷ 109 = 1 remainder 77 |
| 3 | 109 ÷ 77 = 1 remainder 32 |
| 4 | 77 ÷ 32 = 2 remainder 13 |
| 5 | 32 ÷ 13 = 2 remainder 6 |
| 6 | 13 ÷ 6 = 2 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 24 | 192 |
| 75 and 26 | 1950 |
| 172 and 135 | 23220 |
| 70 and 93 | 6510 |
| 182 and 126 | 1638 |