Least Common Multiple (LCM) of 23 and 136
The least common multiple (LCM) of 23 and 136 is 3128.
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 136?
First, calculate the GCD of 23 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 136 = 0 remainder 23 |
| 2 | 136 ÷ 23 = 5 remainder 21 |
| 3 | 23 ÷ 21 = 1 remainder 2 |
| 4 | 21 ÷ 2 = 10 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 196 | 25284 |
| 12 and 56 | 168 |
| 45 and 42 | 630 |
| 84 and 72 | 504 |
| 138 and 66 | 1518 |