Least Common Multiple (LCM) of 23 and 155
The least common multiple (LCM) of 23 and 155 is 3565.
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 155?
First, calculate the GCD of 23 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 155 = 0 remainder 23 |
| 2 | 155 ÷ 23 = 6 remainder 17 |
| 3 | 23 ÷ 17 = 1 remainder 6 |
| 4 | 17 ÷ 6 = 2 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 56 | 560 |
| 118 and 161 | 18998 |
| 94 and 154 | 7238 |
| 45 and 170 | 1530 |
| 132 and 109 | 14388 |