Least Common Multiple (LCM) of 34 and 59
The least common multiple (LCM) of 34 and 59 is 2006.
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 59?
First, calculate the GCD of 34 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 59 = 0 remainder 34 |
| 2 | 59 ÷ 34 = 1 remainder 25 |
| 3 | 34 ÷ 25 = 1 remainder 9 |
| 4 | 25 ÷ 9 = 2 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 196 | 1764 |
| 184 and 17 | 3128 |
| 182 and 41 | 7462 |
| 66 and 16 | 528 |
| 157 and 147 | 23079 |