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 |
|---|---|
| 87 and 74 | 6438 |
| 39 and 14 | 546 |
| 119 and 120 | 14280 |
| 144 and 65 | 9360 |
| 50 and 91 | 4550 |