Least Common Multiple (LCM) of 71 and 101
The least common multiple (LCM) of 71 and 101 is 7171.
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 101?
First, calculate the GCD of 71 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 101 = 0 remainder 71 |
| 2 | 101 ÷ 71 = 1 remainder 30 |
| 3 | 71 ÷ 30 = 2 remainder 11 |
| 4 | 30 ÷ 11 = 2 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 117 | 13923 |
| 74 and 123 | 9102 |
| 14 and 174 | 1218 |
| 55 and 76 | 4180 |
| 50 and 175 | 350 |