Least Common Multiple (LCM) of 192 and 61
The least common multiple (LCM) of 192 and 61 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 192 and 61?
First, calculate the GCD of 192 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 61 = 3 remainder 9 |
| 2 | 61 ÷ 9 = 6 remainder 7 |
| 3 | 9 ÷ 7 = 1 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 110 | 1430 |
| 49 and 61 | 2989 |
| 82 and 172 | 7052 |
| 142 and 187 | 26554 |
| 131 and 132 | 17292 |