Least Common Multiple (LCM) of 34 and 159
The least common multiple (LCM) of 34 and 159 is 5406.
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 159?
First, calculate the GCD of 34 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 159 = 0 remainder 34 |
| 2 | 159 ÷ 34 = 4 remainder 23 |
| 3 | 34 ÷ 23 = 1 remainder 11 |
| 4 | 23 ÷ 11 = 2 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 131 | 13886 |
| 98 and 161 | 2254 |
| 151 and 43 | 6493 |
| 81 and 14 | 1134 |
| 167 and 140 | 23380 |