Least Common Multiple (LCM) of 155 and 123
The least common multiple (LCM) of 155 and 123 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 155 and 123?
First, calculate the GCD of 155 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 155 ÷ 123 = 1 remainder 32 |
| 2 | 123 ÷ 32 = 3 remainder 27 |
| 3 | 32 ÷ 27 = 1 remainder 5 |
| 4 | 27 ÷ 5 = 5 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 160 | 1760 |
| 185 and 67 | 12395 |
| 33 and 162 | 1782 |
| 90 and 178 | 8010 |
| 160 and 83 | 13280 |