Least Common Multiple (LCM) of 136 and 194
The least common multiple (LCM) of 136 and 194 is 13192.
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 194?
First, calculate the GCD of 136 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 194 = 0 remainder 136 |
| 2 | 194 ÷ 136 = 1 remainder 58 |
| 3 | 136 ÷ 58 = 2 remainder 20 |
| 4 | 58 ÷ 20 = 2 remainder 18 |
| 5 | 20 ÷ 18 = 1 remainder 2 |
| 6 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 68 | 2108 |
| 45 and 69 | 1035 |
| 108 and 91 | 9828 |
| 105 and 152 | 15960 |
| 68 and 166 | 5644 |