Least Common Multiple (LCM) of 149 and 113
The least common multiple (LCM) of 149 and 113 is 16837.
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 113?
First, calculate the GCD of 149 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 149 ÷ 113 = 1 remainder 36 |
| 2 | 113 ÷ 36 = 3 remainder 5 |
| 3 | 36 ÷ 5 = 7 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 74 | 5402 |
| 178 and 91 | 16198 |
| 105 and 51 | 1785 |
| 133 and 32 | 4256 |
| 20 and 19 | 380 |