Least Common Multiple (LCM) of 105 and 118
The least common multiple (LCM) of 105 and 118 is 12390.
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 118?
First, calculate the GCD of 105 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 118 = 0 remainder 105 |
| 2 | 118 ÷ 105 = 1 remainder 13 |
| 3 | 105 ÷ 13 = 8 remainder 1 |
| 4 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 26 | 1222 |
| 119 and 82 | 9758 |
| 192 and 164 | 7872 |
| 104 and 113 | 11752 |
| 36 and 194 | 3492 |