Least Common Multiple (LCM) of 105 and 54
The least common multiple (LCM) of 105 and 54 is 1890.
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 105 and 54?
First, calculate the GCD of 105 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 54 = 1 remainder 51 |
| 2 | 54 ÷ 51 = 1 remainder 3 |
| 3 | 51 ÷ 3 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 192 | 3264 |
| 165 and 65 | 2145 |
| 32 and 43 | 1376 |
| 186 and 114 | 3534 |
| 76 and 26 | 988 |