Least Common Multiple (LCM) of 29 and 106
The least common multiple (LCM) of 29 and 106 is 3074.
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 29 and 106?
First, calculate the GCD of 29 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 106 = 0 remainder 29 |
| 2 | 106 ÷ 29 = 3 remainder 19 |
| 3 | 29 ÷ 19 = 1 remainder 10 |
| 4 | 19 ÷ 10 = 1 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 35 | 1400 |
| 180 and 97 | 17460 |
| 53 and 190 | 10070 |
| 42 and 83 | 3486 |
| 43 and 58 | 2494 |