Least Common Multiple (LCM) of 192 and 117
The least common multiple (LCM) of 192 and 117 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 192 and 117?
First, calculate the GCD of 192 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 117 = 1 remainder 75 |
| 2 | 117 ÷ 75 = 1 remainder 42 |
| 3 | 75 ÷ 42 = 1 remainder 33 |
| 4 | 42 ÷ 33 = 1 remainder 9 |
| 5 | 33 ÷ 9 = 3 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 180 | 7740 |
| 18 and 63 | 126 |
| 153 and 121 | 18513 |
| 39 and 183 | 2379 |
| 198 and 165 | 990 |