Least Common Multiple (LCM) of 136 and 195
The least common multiple (LCM) of 136 and 195 is 26520.
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 195?
First, calculate the GCD of 136 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 195 = 0 remainder 136 |
| 2 | 195 ÷ 136 = 1 remainder 59 |
| 3 | 136 ÷ 59 = 2 remainder 18 |
| 4 | 59 ÷ 18 = 3 remainder 5 |
| 5 | 18 ÷ 5 = 3 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 143 | 12870 |
| 103 and 177 | 18231 |
| 167 and 78 | 13026 |
| 152 and 45 | 6840 |
| 72 and 144 | 144 |