Least Common Multiple (LCM) of 180 and 157
The least common multiple (LCM) of 180 and 157 is 28260.
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 157?
First, calculate the GCD of 180 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 157 = 1 remainder 23 |
| 2 | 157 ÷ 23 = 6 remainder 19 |
| 3 | 23 ÷ 19 = 1 remainder 4 |
| 4 | 19 ÷ 4 = 4 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 171 | 2907 |
| 152 and 193 | 29336 |
| 86 and 186 | 7998 |
| 129 and 61 | 7869 |
| 163 and 177 | 28851 |