Least Common Multiple (LCM) of 34 and 160
The least common multiple (LCM) of 34 and 160 is 2720.
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 160?
First, calculate the GCD of 34 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 160 = 0 remainder 34 |
| 2 | 160 ÷ 34 = 4 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 |
|---|---|
| 31 and 123 | 3813 |
| 168 and 195 | 10920 |
| 118 and 46 | 2714 |
| 189 and 55 | 10395 |
| 132 and 105 | 4620 |