Least Common Multiple (LCM) of 136 and 111
The least common multiple (LCM) of 136 and 111 is 15096.
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 136 and 111?
First, calculate the GCD of 136 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 111 = 1 remainder 25 |
| 2 | 111 ÷ 25 = 4 remainder 11 |
| 3 | 25 ÷ 11 = 2 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 96 | 3360 |
| 14 and 180 | 1260 |
| 183 and 165 | 10065 |
| 186 and 108 | 3348 |
| 193 and 134 | 25862 |