Least Common Multiple (LCM) of 180 and 137
The least common multiple (LCM) of 180 and 137 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 180 and 137?
First, calculate the GCD of 180 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 137 = 1 remainder 43 |
| 2 | 137 ÷ 43 = 3 remainder 8 |
| 3 | 43 ÷ 8 = 5 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 90 | 11970 |
| 108 and 142 | 7668 |
| 155 and 128 | 19840 |
| 154 and 128 | 9856 |
| 196 and 63 | 1764 |