Least Common Multiple (LCM) of 91 and 165
The least common multiple (LCM) of 91 and 165 is 15015.
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 165?
First, calculate the GCD of 91 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 165 = 0 remainder 91 |
| 2 | 165 ÷ 91 = 1 remainder 74 |
| 3 | 91 ÷ 74 = 1 remainder 17 |
| 4 | 74 ÷ 17 = 4 remainder 6 |
| 5 | 17 ÷ 6 = 2 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 109 | 19184 |
| 100 and 191 | 19100 |
| 89 and 199 | 17711 |
| 150 and 166 | 12450 |
| 19 and 200 | 3800 |