Least Common Multiple (LCM) of 40 and 193
The least common multiple (LCM) of 40 and 193 is 7720.
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 193?
First, calculate the GCD of 40 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 193 = 0 remainder 40 |
| 2 | 193 ÷ 40 = 4 remainder 33 |
| 3 | 40 ÷ 33 = 1 remainder 7 |
| 4 | 33 ÷ 7 = 4 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 82 | 11070 |
| 112 and 116 | 3248 |
| 150 and 69 | 3450 |
| 78 and 12 | 156 |
| 108 and 63 | 756 |