Least Common Multiple (LCM) of 118 and 190
The least common multiple (LCM) of 118 and 190 is 11210.
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 190?
First, calculate the GCD of 118 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 190 = 0 remainder 118 |
| 2 | 190 ÷ 118 = 1 remainder 72 |
| 3 | 118 ÷ 72 = 1 remainder 46 |
| 4 | 72 ÷ 46 = 1 remainder 26 |
| 5 | 46 ÷ 26 = 1 remainder 20 |
| 6 | 26 ÷ 20 = 1 remainder 6 |
| 7 | 20 ÷ 6 = 3 remainder 2 |
| 8 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 116 | 1740 |
| 37 and 123 | 4551 |
| 45 and 177 | 2655 |
| 58 and 31 | 1798 |
| 169 and 135 | 22815 |