Least Common Multiple (LCM) of 83 and 121
The least common multiple (LCM) of 83 and 121 is 10043.
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 121?
First, calculate the GCD of 83 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 121 = 0 remainder 83 |
| 2 | 121 ÷ 83 = 1 remainder 38 |
| 3 | 83 ÷ 38 = 2 remainder 7 |
| 4 | 38 ÷ 7 = 5 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 138 | 4830 |
| 97 and 119 | 11543 |
| 59 and 110 | 6490 |
| 100 and 177 | 17700 |
| 142 and 169 | 23998 |