Least Common Multiple (LCM) of 135 and 196
The least common multiple (LCM) of 135 and 196 is 26460.
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 196?
First, calculate the GCD of 135 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 196 = 0 remainder 135 |
| 2 | 196 ÷ 135 = 1 remainder 61 |
| 3 | 135 ÷ 61 = 2 remainder 13 |
| 4 | 61 ÷ 13 = 4 remainder 9 |
| 5 | 13 ÷ 9 = 1 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 43 | 3053 |
| 158 and 34 | 2686 |
| 132 and 90 | 1980 |
| 64 and 41 | 2624 |
| 181 and 174 | 31494 |