Least Common Multiple (LCM) of 107 and 29
The least common multiple (LCM) of 107 and 29 is 3103.
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 107 and 29?
First, calculate the GCD of 107 and 29 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 29 = 3 remainder 20 |
| 2 | 29 ÷ 20 = 1 remainder 9 |
| 3 | 20 ÷ 9 = 2 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 93 | 17484 |
| 47 and 154 | 7238 |
| 45 and 141 | 2115 |
| 113 and 103 | 11639 |
| 55 and 153 | 8415 |