Least Common Multiple (LCM) of 71 and 167
The least common multiple (LCM) of 71 and 167 is 11857.
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 167?
First, calculate the GCD of 71 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 167 = 0 remainder 71 |
| 2 | 167 ÷ 71 = 2 remainder 25 |
| 3 | 71 ÷ 25 = 2 remainder 21 |
| 4 | 25 ÷ 21 = 1 remainder 4 |
| 5 | 21 ÷ 4 = 5 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 148 | 16132 |
| 147 and 86 | 12642 |
| 25 and 73 | 1825 |
| 45 and 53 | 2385 |
| 130 and 17 | 2210 |