Least Common Multiple (LCM) of 69 and 192
The least common multiple (LCM) of 69 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 69 and 192?
First, calculate the GCD of 69 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 192 = 0 remainder 69 |
| 2 | 192 ÷ 69 = 2 remainder 54 |
| 3 | 69 ÷ 54 = 1 remainder 15 |
| 4 | 54 ÷ 15 = 3 remainder 9 |
| 5 | 15 ÷ 9 = 1 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 72 | 1152 |
| 123 and 172 | 21156 |
| 104 and 111 | 11544 |
| 192 and 152 | 3648 |
| 150 and 164 | 12300 |