Least Common Multiple (LCM) of 34 and 12
The least common multiple (LCM) of 34 and 12 is 204.
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 12?
First, calculate the GCD of 34 and 12 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 12 = 2 remainder 10 |
| 2 | 12 ÷ 10 = 1 remainder 2 |
| 3 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 53 | 6996 |
| 127 and 106 | 13462 |
| 125 and 95 | 2375 |
| 157 and 189 | 29673 |
| 103 and 66 | 6798 |