Least Common Multiple (LCM) of 81 and 157
The least common multiple (LCM) of 81 and 157 is 12717.
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 81 and 157?
First, calculate the GCD of 81 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 157 = 0 remainder 81 |
| 2 | 157 ÷ 81 = 1 remainder 76 |
| 3 | 81 ÷ 76 = 1 remainder 5 |
| 4 | 76 ÷ 5 = 15 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 50 | 850 |
| 142 and 168 | 11928 |
| 123 and 89 | 10947 |
| 193 and 92 | 17756 |
| 138 and 75 | 3450 |