Least Common Multiple (LCM) of 113 and 189
The least common multiple (LCM) of 113 and 189 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 113 and 189?
First, calculate the GCD of 113 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 189 = 0 remainder 113 |
| 2 | 189 ÷ 113 = 1 remainder 76 |
| 3 | 113 ÷ 76 = 1 remainder 37 |
| 4 | 76 ÷ 37 = 2 remainder 2 |
| 5 | 37 ÷ 2 = 18 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 17 | 3213 |
| 106 and 145 | 15370 |
| 52 and 143 | 572 |
| 55 and 126 | 6930 |
| 164 and 46 | 3772 |