Least Common Multiple (LCM) of 83 and 149
The least common multiple (LCM) of 83 and 149 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 83 and 149?
First, calculate the GCD of 83 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 149 = 0 remainder 83 |
| 2 | 149 ÷ 83 = 1 remainder 66 |
| 3 | 83 ÷ 66 = 1 remainder 17 |
| 4 | 66 ÷ 17 = 3 remainder 15 |
| 5 | 17 ÷ 15 = 1 remainder 2 |
| 6 | 15 ÷ 2 = 7 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 106 | 4770 |
| 181 and 160 | 28960 |
| 123 and 102 | 4182 |
| 119 and 102 | 714 |
| 52 and 134 | 3484 |