Least Common Multiple (LCM) of 34 and 16
The least common multiple (LCM) of 34 and 16 is 272.
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 16?
First, calculate the GCD of 34 and 16 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 16 = 2 remainder 2 |
| 2 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 71 | 8023 |
| 189 and 51 | 3213 |
| 135 and 123 | 5535 |
| 136 and 113 | 15368 |
| 154 and 93 | 14322 |