Least Common Multiple (LCM) of 36 and 192
The least common multiple (LCM) of 36 and 192 is 576.
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 36 and 192?
First, calculate the GCD of 36 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 192 = 0 remainder 36 |
| 2 | 192 ÷ 36 = 5 remainder 12 |
| 3 | 36 ÷ 12 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 57 | 1482 |
| 172 and 184 | 7912 |
| 156 and 120 | 1560 |
| 128 and 10 | 640 |
| 176 and 20 | 880 |