Least Common Multiple (LCM) of 138 and 192
The least common multiple (LCM) of 138 and 192 is 4416.
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 138 and 192?
First, calculate the GCD of 138 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 192 = 0 remainder 138 |
| 2 | 192 ÷ 138 = 1 remainder 54 |
| 3 | 138 ÷ 54 = 2 remainder 30 |
| 4 | 54 ÷ 30 = 1 remainder 24 |
| 5 | 30 ÷ 24 = 1 remainder 6 |
| 6 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 20 | 340 |
| 106 and 73 | 7738 |
| 60 and 146 | 4380 |
| 68 and 98 | 3332 |
| 162 and 175 | 28350 |