Least Common Multiple (LCM) of 165 and 91
The least common multiple (LCM) of 165 and 91 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 165 and 91?
First, calculate the GCD of 165 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 91 = 1 remainder 74 |
| 2 | 91 ÷ 74 = 1 remainder 17 |
| 3 | 74 ÷ 17 = 4 remainder 6 |
| 4 | 17 ÷ 6 = 2 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 47 | 4512 |
| 132 and 78 | 1716 |
| 170 and 136 | 680 |
| 186 and 94 | 8742 |
| 41 and 156 | 6396 |