Least Common Multiple (LCM) of 113 and 188
The least common multiple (LCM) of 113 and 188 is 21244.
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 188?
First, calculate the GCD of 113 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 188 = 0 remainder 113 |
| 2 | 188 ÷ 113 = 1 remainder 75 |
| 3 | 113 ÷ 75 = 1 remainder 38 |
| 4 | 75 ÷ 38 = 1 remainder 37 |
| 5 | 38 ÷ 37 = 1 remainder 1 |
| 6 | 37 ÷ 1 = 37 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 65 | 1560 |
| 120 and 190 | 2280 |
| 35 and 164 | 5740 |
| 103 and 60 | 6180 |
| 136 and 112 | 1904 |