Least Common Multiple (LCM) of 135 and 116
The least common multiple (LCM) of 135 and 116 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 135 and 116?
First, calculate the GCD of 135 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 116 = 1 remainder 19 |
| 2 | 116 ÷ 19 = 6 remainder 2 |
| 3 | 19 ÷ 2 = 9 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 25 | 2975 |
| 76 and 174 | 6612 |
| 11 and 69 | 759 |
| 88 and 108 | 2376 |
| 194 and 107 | 20758 |