Least Common Multiple (LCM) of 188 and 121
The least common multiple (LCM) of 188 and 121 is 22748.
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 121?
First, calculate the GCD of 188 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 121 = 1 remainder 67 |
| 2 | 121 ÷ 67 = 1 remainder 54 |
| 3 | 67 ÷ 54 = 1 remainder 13 |
| 4 | 54 ÷ 13 = 4 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 89 | 6853 |
| 79 and 53 | 4187 |
| 174 and 131 | 22794 |
| 17 and 154 | 2618 |
| 133 and 100 | 13300 |