Least Common Multiple (LCM) of 116 and 157
The least common multiple (LCM) of 116 and 157 is 18212.
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 116 and 157?
First, calculate the GCD of 116 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 157 = 0 remainder 116 |
| 2 | 157 ÷ 116 = 1 remainder 41 |
| 3 | 116 ÷ 41 = 2 remainder 34 |
| 4 | 41 ÷ 34 = 1 remainder 7 |
| 5 | 34 ÷ 7 = 4 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 102 | 17646 |
| 189 and 41 | 7749 |
| 39 and 187 | 7293 |
| 68 and 114 | 3876 |
| 76 and 14 | 532 |