Least Common Multiple (LCM) of 113 and 170
The least common multiple (LCM) of 113 and 170 is 19210.
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 170?
First, calculate the GCD of 113 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 170 = 0 remainder 113 |
| 2 | 170 ÷ 113 = 1 remainder 57 |
| 3 | 113 ÷ 57 = 1 remainder 56 |
| 4 | 57 ÷ 56 = 1 remainder 1 |
| 5 | 56 ÷ 1 = 56 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 100 | 2400 |
| 42 and 197 | 8274 |
| 141 and 140 | 19740 |
| 199 and 142 | 28258 |
| 59 and 162 | 9558 |