Least Common Multiple (LCM) of 185 and 137
The least common multiple (LCM) of 185 and 137 is 25345.
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 185 and 137?
First, calculate the GCD of 185 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 137 = 1 remainder 48 |
| 2 | 137 ÷ 48 = 2 remainder 41 |
| 3 | 48 ÷ 41 = 1 remainder 7 |
| 4 | 41 ÷ 7 = 5 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 17 | 3315 |
| 137 and 17 | 2329 |
| 195 and 176 | 34320 |
| 155 and 19 | 2945 |
| 88 and 170 | 7480 |