Least Common Multiple (LCM) of 123 and 155
The least common multiple (LCM) of 123 and 155 is 19065.
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 123 and 155?
First, calculate the GCD of 123 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 155 = 0 remainder 123 |
| 2 | 155 ÷ 123 = 1 remainder 32 |
| 3 | 123 ÷ 32 = 3 remainder 27 |
| 4 | 32 ÷ 27 = 1 remainder 5 |
| 5 | 27 ÷ 5 = 5 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 95 | 17955 |
| 184 and 32 | 736 |
| 10 and 15 | 30 |
| 113 and 11 | 1243 |
| 77 and 172 | 13244 |