Least Common Multiple (LCM) of 34 and 58
The least common multiple (LCM) of 34 and 58 is 986.
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 58?
First, calculate the GCD of 34 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 58 = 0 remainder 34 |
| 2 | 58 ÷ 34 = 1 remainder 24 |
| 3 | 34 ÷ 24 = 1 remainder 10 |
| 4 | 24 ÷ 10 = 2 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 42 | 2142 |
| 60 and 29 | 1740 |
| 43 and 149 | 6407 |
| 97 and 91 | 8827 |
| 51 and 141 | 2397 |