Least Common Multiple (LCM) of 17 and 91
The least common multiple (LCM) of 17 and 91 is 1547.
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 17 and 91?
First, calculate the GCD of 17 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 91 = 0 remainder 17 |
| 2 | 91 ÷ 17 = 5 remainder 6 |
| 3 | 17 ÷ 6 = 2 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 74 | 9398 |
| 180 and 63 | 1260 |
| 22 and 44 | 44 |
| 85 and 152 | 12920 |
| 153 and 147 | 7497 |