Least Common Multiple (LCM) of 113 and 164
The least common multiple (LCM) of 113 and 164 is 18532.
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 164?
First, calculate the GCD of 113 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 164 = 0 remainder 113 |
| 2 | 164 ÷ 113 = 1 remainder 51 |
| 3 | 113 ÷ 51 = 2 remainder 11 |
| 4 | 51 ÷ 11 = 4 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 155 | 8835 |
| 12 and 63 | 252 |
| 175 and 74 | 12950 |
| 166 and 178 | 14774 |
| 10 and 199 | 1990 |