Least Common Multiple (LCM) of 23 and 135
The least common multiple (LCM) of 23 and 135 is 3105.
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 23 and 135?
First, calculate the GCD of 23 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 135 = 0 remainder 23 |
| 2 | 135 ÷ 23 = 5 remainder 20 |
| 3 | 23 ÷ 20 = 1 remainder 3 |
| 4 | 20 ÷ 3 = 6 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 29 | 4408 |
| 97 and 117 | 11349 |
| 115 and 101 | 11615 |
| 175 and 10 | 350 |
| 74 and 195 | 14430 |