Least Common Multiple (LCM) of 109 and 55
The least common multiple (LCM) of 109 and 55 is 5995.
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 55?
First, calculate the GCD of 109 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 55 = 1 remainder 54 |
| 2 | 55 ÷ 54 = 1 remainder 1 |
| 3 | 54 ÷ 1 = 54 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 110 | 11770 |
| 30 and 128 | 1920 |
| 24 and 167 | 4008 |
| 166 and 140 | 11620 |
| 106 and 101 | 10706 |