Least Common Multiple (LCM) of 123 and 55
The least common multiple (LCM) of 123 and 55 is 6765.
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 55?
First, calculate the GCD of 123 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 55 = 2 remainder 13 |
| 2 | 55 ÷ 13 = 4 remainder 3 |
| 3 | 13 ÷ 3 = 4 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 105 | 420 |
| 71 and 53 | 3763 |
| 176 and 154 | 1232 |
| 124 and 83 | 10292 |
| 53 and 26 | 1378 |