Least Common Multiple (LCM) of 192 and 118
The least common multiple (LCM) of 192 and 118 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 192 and 118?
First, calculate the GCD of 192 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 118 = 1 remainder 74 |
| 2 | 118 ÷ 74 = 1 remainder 44 |
| 3 | 74 ÷ 44 = 1 remainder 30 |
| 4 | 44 ÷ 30 = 1 remainder 14 |
| 5 | 30 ÷ 14 = 2 remainder 2 |
| 6 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 187 | 36278 |
| 118 and 93 | 10974 |
| 119 and 133 | 2261 |
| 35 and 75 | 525 |
| 75 and 54 | 1350 |