Least Common Multiple (LCM) of 137 and 135
The least common multiple (LCM) of 137 and 135 is 18495.
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 137 and 135?
First, calculate the GCD of 137 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 135 = 1 remainder 2 |
| 2 | 135 ÷ 2 = 67 remainder 1 |
| 3 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 19 | 2261 |
| 52 and 102 | 2652 |
| 182 and 21 | 546 |
| 84 and 39 | 1092 |
| 71 and 80 | 5680 |