Least Common Multiple (LCM) of 71 and 55
The least common multiple (LCM) of 71 and 55 is 3905.
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 71 and 55?
First, calculate the GCD of 71 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 55 = 1 remainder 16 |
| 2 | 55 ÷ 16 = 3 remainder 7 |
| 3 | 16 ÷ 7 = 2 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 47 | 7379 |
| 127 and 134 | 17018 |
| 112 and 200 | 2800 |
| 113 and 156 | 17628 |
| 99 and 131 | 12969 |