Least Common Multiple (LCM) of 59 and 192
The least common multiple (LCM) of 59 and 192 is 11328.
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 59 and 192?
First, calculate the GCD of 59 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 192 = 0 remainder 59 |
| 2 | 192 ÷ 59 = 3 remainder 15 |
| 3 | 59 ÷ 15 = 3 remainder 14 |
| 4 | 15 ÷ 14 = 1 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 67 | 6499 |
| 74 and 40 | 1480 |
| 46 and 80 | 1840 |
| 170 and 147 | 24990 |
| 113 and 10 | 1130 |