Least Common Multiple (LCM) of 107 and 34
The least common multiple (LCM) of 107 and 34 is 3638.
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 34?
First, calculate the GCD of 107 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 34 = 3 remainder 5 |
| 2 | 34 ÷ 5 = 6 remainder 4 |
| 3 | 5 ÷ 4 = 1 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 74 | 6438 |
| 174 and 121 | 21054 |
| 42 and 19 | 798 |
| 152 and 43 | 6536 |
| 25 and 134 | 3350 |