Least Common Multiple (LCM) of 71 and 157
The least common multiple (LCM) of 71 and 157 is 11147.
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 157?
First, calculate the GCD of 71 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 157 = 0 remainder 71 |
| 2 | 157 ÷ 71 = 2 remainder 15 |
| 3 | 71 ÷ 15 = 4 remainder 11 |
| 4 | 15 ÷ 11 = 1 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 135 | 18765 |
| 171 and 150 | 8550 |
| 134 and 194 | 12998 |
| 102 and 96 | 1632 |
| 81 and 195 | 5265 |