Least Common Multiple (LCM) of 123 and 40
The least common multiple (LCM) of 123 and 40 is 4920.
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 40?
First, calculate the GCD of 123 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 40 = 3 remainder 3 |
| 2 | 40 ÷ 3 = 13 remainder 1 |
| 3 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 113 | 113 |
| 58 and 31 | 1798 |
| 186 and 166 | 15438 |
| 35 and 166 | 5810 |
| 199 and 175 | 34825 |