Least Common Multiple (LCM) of 137 and 192
The least common multiple (LCM) of 137 and 192 is 26304.
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 137 and 192?
First, calculate the GCD of 137 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 192 = 0 remainder 137 |
| 2 | 192 ÷ 137 = 1 remainder 55 |
| 3 | 137 ÷ 55 = 2 remainder 27 |
| 4 | 55 ÷ 27 = 2 remainder 1 |
| 5 | 27 ÷ 1 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 114 | 4218 |
| 167 and 167 | 167 |
| 91 and 87 | 7917 |
| 174 and 125 | 21750 |
| 75 and 99 | 2475 |