Least Common Multiple (LCM) of 34 and 102
The least common multiple (LCM) of 34 and 102 is 102.
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 34 and 102?
First, calculate the GCD of 34 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 102 = 0 remainder 34 |
| 2 | 102 ÷ 34 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 100 | 12700 |
| 199 and 162 | 32238 |
| 122 and 136 | 8296 |
| 55 and 188 | 10340 |
| 40 and 79 | 3160 |