Least Common Multiple (LCM) of 137 and 173
The least common multiple (LCM) of 137 and 173 is 23701.
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 173?
First, calculate the GCD of 137 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 173 = 0 remainder 137 |
| 2 | 173 ÷ 137 = 1 remainder 36 |
| 3 | 137 ÷ 36 = 3 remainder 29 |
| 4 | 36 ÷ 29 = 1 remainder 7 |
| 5 | 29 ÷ 7 = 4 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 108 | 2700 |
| 55 and 31 | 1705 |
| 103 and 149 | 15347 |
| 164 and 159 | 26076 |
| 45 and 54 | 270 |