Least Common Multiple (LCM) of 118 and 191
The least common multiple (LCM) of 118 and 191 is 22538.
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 191?
First, calculate the GCD of 118 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 191 = 0 remainder 118 |
| 2 | 191 ÷ 118 = 1 remainder 73 |
| 3 | 118 ÷ 73 = 1 remainder 45 |
| 4 | 73 ÷ 45 = 1 remainder 28 |
| 5 | 45 ÷ 28 = 1 remainder 17 |
| 6 | 28 ÷ 17 = 1 remainder 11 |
| 7 | 17 ÷ 11 = 1 remainder 6 |
| 8 | 11 ÷ 6 = 1 remainder 5 |
| 9 | 6 ÷ 5 = 1 remainder 1 |
| 10 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 28 | 1260 |
| 31 and 88 | 2728 |
| 16 and 171 | 2736 |
| 80 and 127 | 10160 |
| 55 and 139 | 7645 |