Least Common Multiple (LCM) of 34 and 49
The least common multiple (LCM) of 34 and 49 is 1666.
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 49?
First, calculate the GCD of 34 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 49 = 0 remainder 34 |
| 2 | 49 ÷ 34 = 1 remainder 15 |
| 3 | 34 ÷ 15 = 2 remainder 4 |
| 4 | 15 ÷ 4 = 3 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 39 | 5187 |
| 129 and 26 | 3354 |
| 163 and 194 | 31622 |
| 131 and 148 | 19388 |
| 121 and 162 | 19602 |