Least Common Multiple (LCM) of 113 and 149
The least common multiple (LCM) of 113 and 149 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 113 and 149?
First, calculate the GCD of 113 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 149 = 0 remainder 113 |
| 2 | 149 ÷ 113 = 1 remainder 36 |
| 3 | 113 ÷ 36 = 3 remainder 5 |
| 4 | 36 ÷ 5 = 7 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 107 | 7811 |
| 160 and 167 | 26720 |
| 114 and 187 | 21318 |
| 174 and 31 | 5394 |
| 11 and 198 | 198 |