Least Common Multiple (LCM) of 71 and 187
The least common multiple (LCM) of 71 and 187 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 71 and 187?
First, calculate the GCD of 71 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 187 = 0 remainder 71 |
| 2 | 187 ÷ 71 = 2 remainder 45 |
| 3 | 71 ÷ 45 = 1 remainder 26 |
| 4 | 45 ÷ 26 = 1 remainder 19 |
| 5 | 26 ÷ 19 = 1 remainder 7 |
| 6 | 19 ÷ 7 = 2 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 19 | 3686 |
| 107 and 36 | 3852 |
| 153 and 133 | 20349 |
| 59 and 133 | 7847 |
| 98 and 69 | 6762 |