Least Common Multiple (LCM) of 34 and 155
The least common multiple (LCM) of 34 and 155 is 5270.
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 155?
First, calculate the GCD of 34 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 155 = 0 remainder 34 |
| 2 | 155 ÷ 34 = 4 remainder 19 |
| 3 | 34 ÷ 19 = 1 remainder 15 |
| 4 | 19 ÷ 15 = 1 remainder 4 |
| 5 | 15 ÷ 4 = 3 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 10 | 1510 |
| 67 and 29 | 1943 |
| 41 and 137 | 5617 |
| 82 and 74 | 3034 |
| 116 and 56 | 1624 |