Least Common Multiple (LCM) of 116 and 123
The least common multiple (LCM) of 116 and 123 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 116 and 123?
First, calculate the GCD of 116 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 123 = 0 remainder 116 |
| 2 | 123 ÷ 116 = 1 remainder 7 |
| 3 | 116 ÷ 7 = 16 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 13 | 377 |
| 148 and 47 | 6956 |
| 149 and 117 | 17433 |
| 36 and 79 | 2844 |
| 195 and 177 | 11505 |