Least Common Multiple (LCM) of 35 and 109
The least common multiple (LCM) of 35 and 109 is 3815.
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 35 and 109?
First, calculate the GCD of 35 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 109 = 0 remainder 35 |
| 2 | 109 ÷ 35 = 3 remainder 4 |
| 3 | 35 ÷ 4 = 8 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 184 | 27416 |
| 72 and 48 | 144 |
| 193 and 67 | 12931 |
| 137 and 17 | 2329 |
| 38 and 102 | 1938 |