Least Common Multiple (LCM) of 123 and 69
The least common multiple (LCM) of 123 and 69 is 2829.
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 69?
First, calculate the GCD of 123 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 69 = 1 remainder 54 |
| 2 | 69 ÷ 54 = 1 remainder 15 |
| 3 | 54 ÷ 15 = 3 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 25 | 4050 |
| 15 and 176 | 2640 |
| 43 and 197 | 8471 |
| 115 and 11 | 1265 |
| 190 and 98 | 9310 |