Least Common Multiple (LCM) of 89 and 113
The least common multiple (LCM) of 89 and 113 is 10057.
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 89 and 113?
First, calculate the GCD of 89 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 113 = 0 remainder 89 |
| 2 | 113 ÷ 89 = 1 remainder 24 |
| 3 | 89 ÷ 24 = 3 remainder 17 |
| 4 | 24 ÷ 17 = 1 remainder 7 |
| 5 | 17 ÷ 7 = 2 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 110 | 1210 |
| 144 and 161 | 23184 |
| 186 and 39 | 2418 |
| 94 and 134 | 6298 |
| 95 and 38 | 190 |