Least Common Multiple (LCM) of 109 and 29
The least common multiple (LCM) of 109 and 29 is 3161.
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 29?
First, calculate the GCD of 109 and 29 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 29 = 3 remainder 22 |
| 2 | 29 ÷ 22 = 1 remainder 7 |
| 3 | 22 ÷ 7 = 3 remainder 1 |
| 4 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 47 | 5170 |
| 31 and 170 | 5270 |
| 43 and 179 | 7697 |
| 109 and 23 | 2507 |
| 154 and 101 | 15554 |