Least Common Multiple (LCM) of 135 and 50
The least common multiple (LCM) of 135 and 50 is 1350.
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 50?
First, calculate the GCD of 135 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 50 = 2 remainder 35 |
| 2 | 50 ÷ 35 = 1 remainder 15 |
| 3 | 35 ÷ 15 = 2 remainder 5 |
| 4 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 102 | 13566 |
| 102 and 182 | 9282 |
| 114 and 169 | 19266 |
| 85 and 185 | 3145 |
| 56 and 66 | 1848 |