Least Common Multiple (LCM) of 187 and 71
The least common multiple (LCM) of 187 and 71 is 13277.
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 187 and 71?
First, calculate the GCD of 187 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 71 = 2 remainder 45 |
| 2 | 71 ÷ 45 = 1 remainder 26 |
| 3 | 45 ÷ 26 = 1 remainder 19 |
| 4 | 26 ÷ 19 = 1 remainder 7 |
| 5 | 19 ÷ 7 = 2 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 133 | 18487 |
| 143 and 177 | 25311 |
| 103 and 83 | 8549 |
| 117 and 68 | 7956 |
| 116 and 152 | 4408 |