Least Common Multiple (LCM) of 40 and 59
The least common multiple (LCM) of 40 and 59 is 2360.
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 59?
First, calculate the GCD of 40 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 59 = 0 remainder 40 |
| 2 | 59 ÷ 40 = 1 remainder 19 |
| 3 | 40 ÷ 19 = 2 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 18 | 1656 |
| 101 and 190 | 19190 |
| 156 and 191 | 29796 |
| 116 and 149 | 17284 |
| 150 and 90 | 450 |