Least Common Multiple (LCM) of 116 and 136
The least common multiple (LCM) of 116 and 136 is 3944.
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 136?
First, calculate the GCD of 116 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 136 = 0 remainder 116 |
| 2 | 136 ÷ 116 = 1 remainder 20 |
| 3 | 116 ÷ 20 = 5 remainder 16 |
| 4 | 20 ÷ 16 = 1 remainder 4 |
| 5 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 16 | 1680 |
| 42 and 144 | 1008 |
| 65 and 166 | 10790 |
| 158 and 150 | 11850 |
| 76 and 170 | 6460 |