Least Common Multiple (LCM) of 171 and 113
The least common multiple (LCM) of 171 and 113 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 171 and 113?
First, calculate the GCD of 171 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 113 = 1 remainder 58 |
| 2 | 113 ÷ 58 = 1 remainder 55 |
| 3 | 58 ÷ 55 = 1 remainder 3 |
| 4 | 55 ÷ 3 = 18 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 59 | 9676 |
| 113 and 48 | 5424 |
| 145 and 194 | 28130 |
| 136 and 66 | 4488 |
| 129 and 10 | 1290 |