Least Common Multiple (LCM) of 149 and 116
The least common multiple (LCM) of 149 and 116 is 17284.
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 116?
First, calculate the GCD of 149 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 149 ÷ 116 = 1 remainder 33 |
| 2 | 116 ÷ 33 = 3 remainder 17 |
| 3 | 33 ÷ 17 = 1 remainder 16 |
| 4 | 17 ÷ 16 = 1 remainder 1 |
| 5 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 180 | 1260 |
| 167 and 172 | 28724 |
| 67 and 132 | 8844 |
| 22 and 157 | 3454 |
| 157 and 116 | 18212 |