Least Common Multiple (LCM) of 135 and 91
The least common multiple (LCM) of 135 and 91 is 12285.
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 91?
First, calculate the GCD of 135 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 91 = 1 remainder 44 |
| 2 | 91 ÷ 44 = 2 remainder 3 |
| 3 | 44 ÷ 3 = 14 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 55 | 5885 |
| 18 and 139 | 2502 |
| 127 and 141 | 17907 |
| 31 and 106 | 3286 |
| 161 and 12 | 1932 |