Least Common Multiple (LCM) of 188 and 122
The least common multiple (LCM) of 188 and 122 is 11468.
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 122?
First, calculate the GCD of 188 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 122 = 1 remainder 66 |
| 2 | 122 ÷ 66 = 1 remainder 56 |
| 3 | 66 ÷ 56 = 1 remainder 10 |
| 4 | 56 ÷ 10 = 5 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 112 | 3024 |
| 11 and 33 | 33 |
| 64 and 127 | 8128 |
| 185 and 23 | 4255 |
| 11 and 183 | 2013 |