Least Common Multiple (LCM) of 137 and 194
The least common multiple (LCM) of 137 and 194 is 26578.
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 137 and 194?
First, calculate the GCD of 137 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 194 = 0 remainder 137 |
| 2 | 194 ÷ 137 = 1 remainder 57 |
| 3 | 137 ÷ 57 = 2 remainder 23 |
| 4 | 57 ÷ 23 = 2 remainder 11 |
| 5 | 23 ÷ 11 = 2 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 101 | 14140 |
| 148 and 155 | 22940 |
| 69 and 69 | 69 |
| 12 and 142 | 852 |
| 33 and 21 | 231 |