Least Common Multiple (LCM) of 188 and 41
The least common multiple (LCM) of 188 and 41 is 7708.
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 41?
First, calculate the GCD of 188 and 41 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 41 = 4 remainder 24 |
| 2 | 41 ÷ 24 = 1 remainder 17 |
| 3 | 24 ÷ 17 = 1 remainder 7 |
| 4 | 17 ÷ 7 = 2 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 99 | 1881 |
| 193 and 129 | 24897 |
| 18 and 180 | 180 |
| 85 and 138 | 11730 |
| 153 and 87 | 4437 |