Least Common Multiple (LCM) of 91 and 180
The least common multiple (LCM) of 91 and 180 is 16380.
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 91 and 180?
First, calculate the GCD of 91 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 180 = 0 remainder 91 |
| 2 | 180 ÷ 91 = 1 remainder 89 |
| 3 | 91 ÷ 89 = 1 remainder 2 |
| 4 | 89 ÷ 2 = 44 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 21 | 3570 |
| 20 and 182 | 1820 |
| 159 and 65 | 10335 |
| 119 and 192 | 22848 |
| 95 and 92 | 8740 |