Least Common Multiple (LCM) of 91 and 55
The least common multiple (LCM) of 91 and 55 is 5005.
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 55?
First, calculate the GCD of 91 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 55 = 1 remainder 36 |
| 2 | 55 ÷ 36 = 1 remainder 19 |
| 3 | 36 ÷ 19 = 1 remainder 17 |
| 4 | 19 ÷ 17 = 1 remainder 2 |
| 5 | 17 ÷ 2 = 8 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 136 | 680 |
| 21 and 10 | 210 |
| 182 and 63 | 1638 |
| 55 and 172 | 9460 |
| 150 and 94 | 7050 |