Least Common Multiple (LCM) of 186 and 71
The least common multiple (LCM) of 186 and 71 is 13206.
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 186 and 71?
First, calculate the GCD of 186 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 71 = 2 remainder 44 |
| 2 | 71 ÷ 44 = 1 remainder 27 |
| 3 | 44 ÷ 27 = 1 remainder 17 |
| 4 | 27 ÷ 17 = 1 remainder 10 |
| 5 | 17 ÷ 10 = 1 remainder 7 |
| 6 | 10 ÷ 7 = 1 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 92 and 22 | 1012 |
| 95 and 70 | 1330 |
| 82 and 186 | 7626 |
| 108 and 161 | 17388 |
| 170 and 51 | 510 |