Least Common Multiple (LCM) of 188 and 117
The least common multiple (LCM) of 188 and 117 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 188 and 117?
First, calculate the GCD of 188 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 117 = 1 remainder 71 |
| 2 | 117 ÷ 71 = 1 remainder 46 |
| 3 | 71 ÷ 46 = 1 remainder 25 |
| 4 | 46 ÷ 25 = 1 remainder 21 |
| 5 | 25 ÷ 21 = 1 remainder 4 |
| 6 | 21 ÷ 4 = 5 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 107 | 14338 |
| 106 and 65 | 6890 |
| 79 and 162 | 12798 |
| 78 and 44 | 1716 |
| 188 and 168 | 7896 |