Least Common Multiple (LCM) of 118 and 105
The least common multiple (LCM) of 118 and 105 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 118 and 105?
First, calculate the GCD of 118 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 105 = 1 remainder 13 |
| 2 | 105 ÷ 13 = 8 remainder 1 |
| 3 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 81 | 14013 |
| 26 and 83 | 2158 |
| 156 and 60 | 780 |
| 141 and 62 | 8742 |
| 22 and 31 | 682 |