Least Common Multiple (LCM) of 116 and 188
The least common multiple (LCM) of 116 and 188 is 5452.
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 116 and 188?
First, calculate the GCD of 116 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 188 = 0 remainder 116 |
| 2 | 188 ÷ 116 = 1 remainder 72 |
| 3 | 116 ÷ 72 = 1 remainder 44 |
| 4 | 72 ÷ 44 = 1 remainder 28 |
| 5 | 44 ÷ 28 = 1 remainder 16 |
| 6 | 28 ÷ 16 = 1 remainder 12 |
| 7 | 16 ÷ 12 = 1 remainder 4 |
| 8 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 75 | 4050 |
| 52 and 78 | 156 |
| 129 and 14 | 1806 |
| 75 and 28 | 2100 |
| 128 and 174 | 11136 |