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 |
|---|---|
| 66 and 75 | 1650 |
| 138 and 57 | 2622 |
| 32 and 146 | 2336 |
| 123 and 197 | 24231 |
| 186 and 102 | 3162 |