Least Common Multiple (LCM) of 109 and 35
The least common multiple (LCM) of 109 and 35 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 109 and 35?
First, calculate the GCD of 109 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 35 = 3 remainder 4 |
| 2 | 35 ÷ 4 = 8 remainder 3 |
| 3 | 4 ÷ 3 = 1 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 62 | 3348 |
| 126 and 130 | 8190 |
| 44 and 142 | 3124 |
| 14 and 40 | 280 |
| 73 and 119 | 8687 |