Least Common Multiple (LCM) of 71 and 188
The least common multiple (LCM) of 71 and 188 is 13348.
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 71 and 188?
First, calculate the GCD of 71 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 188 = 0 remainder 71 |
| 2 | 188 ÷ 71 = 2 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 |
|---|---|
| 96 and 165 | 5280 |
| 93 and 10 | 930 |
| 135 and 63 | 945 |
| 131 and 80 | 10480 |
| 123 and 125 | 15375 |