Least Common Multiple (LCM) of 149 and 83
The least common multiple (LCM) of 149 and 83 is 12367.
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 83?
First, calculate the GCD of 149 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 149 ÷ 83 = 1 remainder 66 |
| 2 | 83 ÷ 66 = 1 remainder 17 |
| 3 | 66 ÷ 17 = 3 remainder 15 |
| 4 | 17 ÷ 15 = 1 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 113 | 4859 |
| 183 and 107 | 19581 |
| 52 and 100 | 1300 |
| 170 and 194 | 16490 |
| 38 and 70 | 1330 |