Least Common Multiple (LCM) of 109 and 134
The least common multiple (LCM) of 109 and 134 is 14606.
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 134?
First, calculate the GCD of 109 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 134 = 0 remainder 109 |
| 2 | 134 ÷ 109 = 1 remainder 25 |
| 3 | 109 ÷ 25 = 4 remainder 9 |
| 4 | 25 ÷ 9 = 2 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 174 | 6090 |
| 172 and 124 | 5332 |
| 198 and 52 | 5148 |
| 117 and 121 | 14157 |
| 171 and 184 | 31464 |