Least Common Multiple (LCM) of 37 and 193
The least common multiple (LCM) of 37 and 193 is 7141.
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 37 and 193?
First, calculate the GCD of 37 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 193 = 0 remainder 37 |
| 2 | 193 ÷ 37 = 5 remainder 8 |
| 3 | 37 ÷ 8 = 4 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 107 | 2889 |
| 79 and 135 | 10665 |
| 115 and 144 | 16560 |
| 41 and 128 | 5248 |
| 114 and 20 | 1140 |