Least Common Multiple (LCM) of 91 and 170
The least common multiple (LCM) of 91 and 170 is 15470.
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 170?
First, calculate the GCD of 91 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 170 = 0 remainder 91 |
| 2 | 170 ÷ 91 = 1 remainder 79 |
| 3 | 91 ÷ 79 = 1 remainder 12 |
| 4 | 79 ÷ 12 = 6 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 144 | 720 |
| 164 and 123 | 492 |
| 23 and 20 | 460 |
| 78 and 186 | 2418 |
| 170 and 169 | 28730 |