Least Common Multiple (LCM) of 116 and 189
The least common multiple (LCM) of 116 and 189 is 21924.
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 116 and 189?
First, calculate the GCD of 116 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 189 = 0 remainder 116 |
| 2 | 189 ÷ 116 = 1 remainder 73 |
| 3 | 116 ÷ 73 = 1 remainder 43 |
| 4 | 73 ÷ 43 = 1 remainder 30 |
| 5 | 43 ÷ 30 = 1 remainder 13 |
| 6 | 30 ÷ 13 = 2 remainder 4 |
| 7 | 13 ÷ 4 = 3 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 111 | 9213 |
| 108 and 31 | 3348 |
| 22 and 51 | 1122 |
| 15 and 164 | 2460 |
| 120 and 71 | 8520 |