Least Common Multiple (LCM) of 196 and 135
The least common multiple (LCM) of 196 and 135 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 196 and 135?
First, calculate the GCD of 196 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 135 = 1 remainder 61 |
| 2 | 135 ÷ 61 = 2 remainder 13 |
| 3 | 61 ÷ 13 = 4 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 192 | 26304 |
| 199 and 15 | 2985 |
| 108 and 102 | 1836 |
| 99 and 161 | 15939 |
| 60 and 69 | 1380 |