Least Common Multiple (LCM) of 113 and 171
The least common multiple (LCM) of 113 and 171 is 19323.
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 113 and 171?
First, calculate the GCD of 113 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 171 = 0 remainder 113 |
| 2 | 171 ÷ 113 = 1 remainder 58 |
| 3 | 113 ÷ 58 = 1 remainder 55 |
| 4 | 58 ÷ 55 = 1 remainder 3 |
| 5 | 55 ÷ 3 = 18 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 28 | 140 |
| 60 and 67 | 4020 |
| 138 and 27 | 1242 |
| 29 and 145 | 145 |
| 92 and 117 | 10764 |