Least Common Multiple (LCM) of 113 and 166
The least common multiple (LCM) of 113 and 166 is 18758.
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 166?
First, calculate the GCD of 113 and 166 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 166 = 0 remainder 113 |
| 2 | 166 ÷ 113 = 1 remainder 53 |
| 3 | 113 ÷ 53 = 2 remainder 7 |
| 4 | 53 ÷ 7 = 7 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 75 | 2100 |
| 145 and 123 | 17835 |
| 148 and 148 | 148 |
| 193 and 107 | 20651 |
| 21 and 62 | 1302 |