Least Common Multiple (LCM) of 109 and 54
The least common multiple (LCM) of 109 and 54 is 5886.
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 109 and 54?
First, calculate the GCD of 109 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 54 = 2 remainder 1 |
| 2 | 54 ÷ 1 = 54 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 113 | 13560 |
| 81 and 16 | 1296 |
| 174 and 183 | 10614 |
| 101 and 162 | 16362 |
| 98 and 164 | 8036 |