Least Common Multiple (LCM) of 189 and 113
The least common multiple (LCM) of 189 and 113 is 21357.
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 113?
First, calculate the GCD of 189 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 113 = 1 remainder 76 |
| 2 | 113 ÷ 76 = 1 remainder 37 |
| 3 | 76 ÷ 37 = 2 remainder 2 |
| 4 | 37 ÷ 2 = 18 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 56 | 336 |
| 55 and 56 | 3080 |
| 18 and 82 | 738 |
| 164 and 189 | 30996 |
| 128 and 71 | 9088 |