Least Common Multiple (LCM) of 55 and 91
The least common multiple (LCM) of 55 and 91 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 55 and 91?
First, calculate the GCD of 55 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 91 = 0 remainder 55 |
| 2 | 91 ÷ 55 = 1 remainder 36 |
| 3 | 55 ÷ 36 = 1 remainder 19 |
| 4 | 36 ÷ 19 = 1 remainder 17 |
| 5 | 19 ÷ 17 = 1 remainder 2 |
| 6 | 17 ÷ 2 = 8 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 167 | 2171 |
| 51 and 31 | 1581 |
| 86 and 38 | 1634 |
| 195 and 27 | 1755 |
| 12 and 181 | 2172 |