Least Common Multiple (LCM) of 114 and 188
The least common multiple (LCM) of 114 and 188 is 10716.
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 114 and 188?
First, calculate the GCD of 114 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 188 = 0 remainder 114 |
| 2 | 188 ÷ 114 = 1 remainder 74 |
| 3 | 114 ÷ 74 = 1 remainder 40 |
| 4 | 74 ÷ 40 = 1 remainder 34 |
| 5 | 40 ÷ 34 = 1 remainder 6 |
| 6 | 34 ÷ 6 = 5 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 20 | 220 |
| 134 and 99 | 13266 |
| 109 and 37 | 4033 |
| 141 and 149 | 21009 |
| 45 and 166 | 7470 |