Least Common Multiple (LCM) of 121 and 188
The least common multiple (LCM) of 121 and 188 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 121 and 188?
First, calculate the GCD of 121 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 188 = 0 remainder 121 |
| 2 | 188 ÷ 121 = 1 remainder 67 |
| 3 | 121 ÷ 67 = 1 remainder 54 |
| 4 | 67 ÷ 54 = 1 remainder 13 |
| 5 | 54 ÷ 13 = 4 remainder 2 |
| 6 | 13 ÷ 2 = 6 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 123 | 4305 |
| 151 and 100 | 15100 |
| 21 and 99 | 693 |
| 87 and 107 | 9309 |
| 67 and 189 | 12663 |