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 |
|---|---|
| 175 and 102 | 17850 |
| 106 and 35 | 3710 |
| 85 and 80 | 1360 |
| 76 and 166 | 6308 |
| 141 and 80 | 11280 |