Least Common Multiple (LCM) of 123 and 102
The least common multiple (LCM) of 123 and 102 is 4182.
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 102?
First, calculate the GCD of 123 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 102 = 1 remainder 21 |
| 2 | 102 ÷ 21 = 4 remainder 18 |
| 3 | 21 ÷ 18 = 1 remainder 3 |
| 4 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 144 | 2448 |
| 25 and 139 | 3475 |
| 171 and 59 | 10089 |
| 69 and 114 | 2622 |
| 105 and 35 | 105 |