Least Common Multiple (LCM) of 80 and 154
The least common multiple (LCM) of 80 and 154 is 6160.
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 80 and 154?
First, calculate the GCD of 80 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 154 = 0 remainder 80 |
| 2 | 154 ÷ 80 = 1 remainder 74 |
| 3 | 80 ÷ 74 = 1 remainder 6 |
| 4 | 74 ÷ 6 = 12 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 156 | 6396 |
| 29 and 110 | 3190 |
| 20 and 75 | 300 |
| 47 and 160 | 7520 |
| 45 and 114 | 1710 |