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 |
|---|---|
| 60 and 164 | 2460 |
| 165 and 61 | 10065 |
| 73 and 171 | 12483 |
| 169 and 62 | 10478 |
| 141 and 156 | 7332 |