Least Common Multiple (LCM) of 61 and 192
The least common multiple (LCM) of 61 and 192 is 11712.
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 61 and 192?
First, calculate the GCD of 61 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 192 = 0 remainder 61 |
| 2 | 192 ÷ 61 = 3 remainder 9 |
| 3 | 61 ÷ 9 = 6 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 105 | 18060 |
| 147 and 137 | 20139 |
| 61 and 53 | 3233 |
| 37 and 50 | 1850 |
| 157 and 200 | 31400 |