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 |
|---|---|
| 151 and 198 | 29898 |
| 175 and 117 | 20475 |
| 86 and 142 | 6106 |
| 88 and 160 | 1760 |
| 49 and 64 | 3136 |