Least Common Multiple (LCM) of 40 and 58
The least common multiple (LCM) of 40 and 58 is 1160.
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 58?
First, calculate the GCD of 40 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 58 = 0 remainder 40 |
| 2 | 58 ÷ 40 = 1 remainder 18 |
| 3 | 40 ÷ 18 = 2 remainder 4 |
| 4 | 18 ÷ 4 = 4 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 81 | 3726 |
| 128 and 100 | 3200 |
| 126 and 55 | 6930 |
| 168 and 130 | 10920 |
| 116 and 109 | 12644 |