Least Common Multiple (LCM) of 189 and 118
The least common multiple (LCM) of 189 and 118 is 22302.
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 118?
First, calculate the GCD of 189 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 118 = 1 remainder 71 |
| 2 | 118 ÷ 71 = 1 remainder 47 |
| 3 | 71 ÷ 47 = 1 remainder 24 |
| 4 | 47 ÷ 24 = 1 remainder 23 |
| 5 | 24 ÷ 23 = 1 remainder 1 |
| 6 | 23 ÷ 1 = 23 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 163 | 31296 |
| 180 and 155 | 5580 |
| 93 and 53 | 4929 |
| 119 and 81 | 9639 |
| 137 and 168 | 23016 |