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 |
|---|---|
| 64 and 174 | 5568 |
| 143 and 26 | 286 |
| 74 and 138 | 5106 |
| 178 and 200 | 17800 |
| 129 and 36 | 1548 |