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 |
|---|---|
| 84 and 148 | 3108 |
| 109 and 25 | 2725 |
| 100 and 78 | 3900 |
| 30 and 43 | 1290 |
| 170 and 75 | 2550 |