Least Common Multiple (LCM) of 34 and 61
The least common multiple (LCM) of 34 and 61 is 2074.
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 61?
First, calculate the GCD of 34 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 61 = 0 remainder 34 |
| 2 | 61 ÷ 34 = 1 remainder 27 |
| 3 | 34 ÷ 27 = 1 remainder 7 |
| 4 | 27 ÷ 7 = 3 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 70 | 140 |
| 53 and 103 | 5459 |
| 18 and 38 | 342 |
| 27 and 153 | 459 |
| 140 and 168 | 840 |