Least Common Multiple (LCM) of 34 and 154
The least common multiple (LCM) of 34 and 154 is 2618.
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 154?
First, calculate the GCD of 34 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 154 = 0 remainder 34 |
| 2 | 154 ÷ 34 = 4 remainder 18 |
| 3 | 34 ÷ 18 = 1 remainder 16 |
| 4 | 18 ÷ 16 = 1 remainder 2 |
| 5 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 78 | 5772 |
| 92 and 100 | 2300 |
| 181 and 117 | 21177 |
| 122 and 58 | 3538 |
| 59 and 115 | 6785 |