Least Common Multiple (LCM) of 85 and 188
The least common multiple (LCM) of 85 and 188 is 15980.
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 85 and 188?
First, calculate the GCD of 85 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 188 = 0 remainder 85 |
| 2 | 188 ÷ 85 = 2 remainder 18 |
| 3 | 85 ÷ 18 = 4 remainder 13 |
| 4 | 18 ÷ 13 = 1 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 100 | 10900 |
| 177 and 145 | 25665 |
| 29 and 87 | 87 |
| 95 and 105 | 1995 |
| 155 and 66 | 10230 |