Least Common Multiple (LCM) of 192 and 121
The least common multiple (LCM) of 192 and 121 is 23232.
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 121?
First, calculate the GCD of 192 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 121 = 1 remainder 71 |
| 2 | 121 ÷ 71 = 1 remainder 50 |
| 3 | 71 ÷ 50 = 1 remainder 21 |
| 4 | 50 ÷ 21 = 2 remainder 8 |
| 5 | 21 ÷ 8 = 2 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 164 | 31980 |
| 40 and 16 | 80 |
| 144 and 170 | 12240 |
| 26 and 67 | 1742 |
| 100 and 166 | 8300 |