Least Common Multiple (LCM) of 105 and 113
The least common multiple (LCM) of 105 and 113 is 11865.
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 105 and 113?
First, calculate the GCD of 105 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 113 = 0 remainder 105 |
| 2 | 113 ÷ 105 = 1 remainder 8 |
| 3 | 105 ÷ 8 = 13 remainder 1 |
| 4 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 179 | 5370 |
| 138 and 191 | 26358 |
| 138 and 90 | 2070 |
| 124 and 70 | 4340 |
| 74 and 177 | 13098 |