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 |
|---|---|
| 100 and 85 | 1700 |
| 36 and 11 | 396 |
| 147 and 82 | 12054 |
| 106 and 156 | 8268 |
| 126 and 33 | 1386 |