Least Common Multiple (LCM) of 113 and 168
The least common multiple (LCM) of 113 and 168 is 18984.
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 168?
First, calculate the GCD of 113 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 168 = 0 remainder 113 |
| 2 | 168 ÷ 113 = 1 remainder 55 |
| 3 | 113 ÷ 55 = 2 remainder 3 |
| 4 | 55 ÷ 3 = 18 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 185 | 19980 |
| 57 and 189 | 3591 |
| 44 and 20 | 220 |
| 182 and 89 | 16198 |
| 63 and 107 | 6741 |