Least Common Multiple (LCM) of 40 and 123
The least common multiple (LCM) of 40 and 123 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 40 and 123?
First, calculate the GCD of 40 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 123 = 0 remainder 40 |
| 2 | 123 ÷ 40 = 3 remainder 3 |
| 3 | 40 ÷ 3 = 13 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 58 | 10266 |
| 116 and 113 | 13108 |
| 171 and 178 | 30438 |
| 68 and 39 | 2652 |
| 178 and 82 | 7298 |