Least Common Multiple (LCM) of 135 and 161
The least common multiple (LCM) of 135 and 161 is 21735.
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 161?
First, calculate the GCD of 135 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 161 = 0 remainder 135 |
| 2 | 161 ÷ 135 = 1 remainder 26 |
| 3 | 135 ÷ 26 = 5 remainder 5 |
| 4 | 26 ÷ 5 = 5 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 135 | 4320 |
| 127 and 88 | 11176 |
| 85 and 100 | 1700 |
| 105 and 51 | 1785 |
| 17 and 72 | 1224 |