Least Common Multiple (LCM) of 123 and 116
The least common multiple (LCM) of 123 and 116 is 14268.
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 116?
First, calculate the GCD of 123 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 116 = 1 remainder 7 |
| 2 | 116 ÷ 7 = 16 remainder 4 |
| 3 | 7 ÷ 4 = 1 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 73 | 8833 |
| 117 and 33 | 1287 |
| 28 and 115 | 3220 |
| 63 and 166 | 10458 |
| 68 and 45 | 3060 |