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 |
|---|---|
| 165 and 18 | 990 |
| 45 and 122 | 5490 |
| 90 and 120 | 360 |
| 150 and 47 | 7050 |
| 122 and 78 | 4758 |