Least Common Multiple (LCM) of 189 and 116
The least common multiple (LCM) of 189 and 116 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 189 and 116?
First, calculate the GCD of 189 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 116 = 1 remainder 73 |
| 2 | 116 ÷ 73 = 1 remainder 43 |
| 3 | 73 ÷ 43 = 1 remainder 30 |
| 4 | 43 ÷ 30 = 1 remainder 13 |
| 5 | 30 ÷ 13 = 2 remainder 4 |
| 6 | 13 ÷ 4 = 3 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 126 | 7308 |
| 86 and 177 | 15222 |
| 22 and 70 | 770 |
| 110 and 48 | 2640 |
| 168 and 36 | 504 |