Least Common Multiple (LCM) of 135 and 97
The least common multiple (LCM) of 135 and 97 is 13095.
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 97?
First, calculate the GCD of 135 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 97 = 1 remainder 38 |
| 2 | 97 ÷ 38 = 2 remainder 21 |
| 3 | 38 ÷ 21 = 1 remainder 17 |
| 4 | 21 ÷ 17 = 1 remainder 4 |
| 5 | 17 ÷ 4 = 4 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 171 | 27531 |
| 43 and 38 | 1634 |
| 66 and 105 | 2310 |
| 44 and 11 | 44 |
| 88 and 195 | 17160 |