Least Common Multiple (LCM) of 117 and 192
The least common multiple (LCM) of 117 and 192 is 7488.
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 117 and 192?
First, calculate the GCD of 117 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 192 = 0 remainder 117 |
| 2 | 192 ÷ 117 = 1 remainder 75 |
| 3 | 117 ÷ 75 = 1 remainder 42 |
| 4 | 75 ÷ 42 = 1 remainder 33 |
| 5 | 42 ÷ 33 = 1 remainder 9 |
| 6 | 33 ÷ 9 = 3 remainder 6 |
| 7 | 9 ÷ 6 = 1 remainder 3 |
| 8 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 72 | 792 |
| 156 and 162 | 4212 |
| 184 and 93 | 17112 |
| 118 and 197 | 23246 |
| 31 and 142 | 4402 |