Least Common Multiple (LCM) of 71 and 113
The least common multiple (LCM) of 71 and 113 is 8023.
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 113?
First, calculate the GCD of 71 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 113 = 0 remainder 71 |
| 2 | 113 ÷ 71 = 1 remainder 42 |
| 3 | 71 ÷ 42 = 1 remainder 29 |
| 4 | 42 ÷ 29 = 1 remainder 13 |
| 5 | 29 ÷ 13 = 2 remainder 3 |
| 6 | 13 ÷ 3 = 4 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 40 | 1320 |
| 196 and 36 | 1764 |
| 56 and 58 | 1624 |
| 23 and 103 | 2369 |
| 73 and 98 | 7154 |