Least Common Multiple (LCM) of 137 and 180
The least common multiple (LCM) of 137 and 180 is 24660.
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 180?
First, calculate the GCD of 137 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 180 = 0 remainder 137 |
| 2 | 180 ÷ 137 = 1 remainder 43 |
| 3 | 137 ÷ 43 = 3 remainder 8 |
| 4 | 43 ÷ 8 = 5 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 43 | 1548 |
| 146 and 174 | 12702 |
| 96 and 195 | 6240 |
| 157 and 81 | 12717 |
| 156 and 121 | 18876 |