Least Common Multiple (LCM) of 118 and 192
The least common multiple (LCM) of 118 and 192 is 11328.
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 192?
First, calculate the GCD of 118 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 192 = 0 remainder 118 |
| 2 | 192 ÷ 118 = 1 remainder 74 |
| 3 | 118 ÷ 74 = 1 remainder 44 |
| 4 | 74 ÷ 44 = 1 remainder 30 |
| 5 | 44 ÷ 30 = 1 remainder 14 |
| 6 | 30 ÷ 14 = 2 remainder 2 |
| 7 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 104 | 20696 |
| 137 and 172 | 23564 |
| 123 and 97 | 11931 |
| 16 and 150 | 1200 |
| 21 and 89 | 1869 |