Least Common Multiple (LCM) of 157 and 86
The least common multiple (LCM) of 157 and 86 is 13502.
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 157 and 86?
First, calculate the GCD of 157 and 86 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 86 = 1 remainder 71 |
| 2 | 86 ÷ 71 = 1 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 |
|---|---|
| 108 and 46 | 2484 |
| 81 and 104 | 8424 |
| 105 and 95 | 1995 |
| 108 and 143 | 15444 |
| 28 and 103 | 2884 |