Least Common Multiple (LCM) of 34 and 156
The least common multiple (LCM) of 34 and 156 is 2652.
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 156?
First, calculate the GCD of 34 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 156 = 0 remainder 34 |
| 2 | 156 ÷ 34 = 4 remainder 20 |
| 3 | 34 ÷ 20 = 1 remainder 14 |
| 4 | 20 ÷ 14 = 1 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 186 | 14322 |
| 197 and 42 | 8274 |
| 101 and 91 | 9191 |
| 192 and 101 | 19392 |
| 80 and 165 | 2640 |