Least Common Multiple (LCM) of 123 and 126
The least common multiple (LCM) of 123 and 126 is 5166.
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 126?
First, calculate the GCD of 123 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 126 = 0 remainder 123 |
| 2 | 126 ÷ 123 = 1 remainder 3 |
| 3 | 123 ÷ 3 = 41 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 147 | 441 |
| 164 and 153 | 25092 |
| 144 and 178 | 12816 |
| 50 and 45 | 450 |
| 108 and 166 | 8964 |