Least Common Multiple (LCM) of 188 and 118
The least common multiple (LCM) of 188 and 118 is 11092.
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 188 and 118?
First, calculate the GCD of 188 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 118 = 1 remainder 70 |
| 2 | 118 ÷ 70 = 1 remainder 48 |
| 3 | 70 ÷ 48 = 1 remainder 22 |
| 4 | 48 ÷ 22 = 2 remainder 4 |
| 5 | 22 ÷ 4 = 5 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 77 | 5005 |
| 145 and 124 | 17980 |
| 112 and 28 | 112 |
| 105 and 191 | 20055 |
| 80 and 67 | 5360 |