Least Common Multiple (LCM) of 80 and 149
The least common multiple (LCM) of 80 and 149 is 11920.
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 149?
First, calculate the GCD of 80 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 149 = 0 remainder 80 |
| 2 | 149 ÷ 80 = 1 remainder 69 |
| 3 | 80 ÷ 69 = 1 remainder 11 |
| 4 | 69 ÷ 11 = 6 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 108 | 756 |
| 35 and 113 | 3955 |
| 171 and 101 | 17271 |
| 48 and 35 | 1680 |
| 105 and 177 | 6195 |