Least Common Multiple (LCM) of 116 and 135
The least common multiple (LCM) of 116 and 135 is 15660.
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 135?
First, calculate the GCD of 116 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 135 = 0 remainder 116 |
| 2 | 135 ÷ 116 = 1 remainder 19 |
| 3 | 116 ÷ 19 = 6 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 193 | 33003 |
| 83 and 112 | 9296 |
| 19 and 66 | 1254 |
| 140 and 165 | 4620 |
| 145 and 58 | 290 |