Least Common Multiple (LCM) of 121 and 192
The least common multiple (LCM) of 121 and 192 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 121 and 192?
First, calculate the GCD of 121 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 192 = 0 remainder 121 |
| 2 | 192 ÷ 121 = 1 remainder 71 |
| 3 | 121 ÷ 71 = 1 remainder 50 |
| 4 | 71 ÷ 50 = 1 remainder 21 |
| 5 | 50 ÷ 21 = 2 remainder 8 |
| 6 | 21 ÷ 8 = 2 remainder 5 |
| 7 | 8 ÷ 5 = 1 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 192 | 24000 |
| 131 and 105 | 13755 |
| 34 and 33 | 1122 |
| 160 and 102 | 8160 |
| 171 and 191 | 32661 |