Least Common Multiple (LCM) of 149 and 180
The least common multiple (LCM) of 149 and 180 is 26820.
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 149 and 180?
First, calculate the GCD of 149 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 149 ÷ 180 = 0 remainder 149 |
| 2 | 180 ÷ 149 = 1 remainder 31 |
| 3 | 149 ÷ 31 = 4 remainder 25 |
| 4 | 31 ÷ 25 = 1 remainder 6 |
| 5 | 25 ÷ 6 = 4 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 95 | 190 |
| 191 and 134 | 25594 |
| 137 and 115 | 15755 |
| 105 and 103 | 10815 |
| 49 and 78 | 3822 |