Least Common Multiple (LCM) of 117 and 188
The least common multiple (LCM) of 117 and 188 is 21996.
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 117 and 188?
First, calculate the GCD of 117 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 188 = 0 remainder 117 |
| 2 | 188 ÷ 117 = 1 remainder 71 |
| 3 | 117 ÷ 71 = 1 remainder 46 |
| 4 | 71 ÷ 46 = 1 remainder 25 |
| 5 | 46 ÷ 25 = 1 remainder 21 |
| 6 | 25 ÷ 21 = 1 remainder 4 |
| 7 | 21 ÷ 4 = 5 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 178 | 3560 |
| 11 and 165 | 165 |
| 99 and 113 | 11187 |
| 110 and 130 | 1430 |
| 34 and 66 | 1122 |