Least Common Multiple (LCM) of 40 and 137
The least common multiple (LCM) of 40 and 137 is 5480.
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 137?
First, calculate the GCD of 40 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 137 = 0 remainder 40 |
| 2 | 137 ÷ 40 = 3 remainder 17 |
| 3 | 40 ÷ 17 = 2 remainder 6 |
| 4 | 17 ÷ 6 = 2 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 199 | 20895 |
| 23 and 96 | 2208 |
| 82 and 174 | 7134 |
| 106 and 22 | 1166 |
| 45 and 180 | 180 |