Least Common Multiple (LCM) of 116 and 149
The least common multiple (LCM) of 116 and 149 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 116 and 149?
First, calculate the GCD of 116 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 149 = 0 remainder 116 |
| 2 | 149 ÷ 116 = 1 remainder 33 |
| 3 | 116 ÷ 33 = 3 remainder 17 |
| 4 | 33 ÷ 17 = 1 remainder 16 |
| 5 | 17 ÷ 16 = 1 remainder 1 |
| 6 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 70 | 350 |
| 73 and 136 | 9928 |
| 155 and 115 | 3565 |
| 15 and 35 | 105 |
| 118 and 137 | 16166 |