Least Common Multiple (LCM) of 155 and 68
The least common multiple (LCM) of 155 and 68 is 10540.
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 155 and 68?
First, calculate the GCD of 155 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 155 ÷ 68 = 2 remainder 19 |
| 2 | 68 ÷ 19 = 3 remainder 11 |
| 3 | 19 ÷ 11 = 1 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 104 | 1560 |
| 109 and 151 | 16459 |
| 45 and 68 | 3060 |
| 169 and 69 | 11661 |
| 193 and 31 | 5983 |