Least Common Multiple (LCM) of 121 and 83
The least common multiple (LCM) of 121 and 83 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 121 and 83?
First, calculate the GCD of 121 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 83 = 1 remainder 38 |
| 2 | 83 ÷ 38 = 2 remainder 7 |
| 3 | 38 ÷ 7 = 5 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 113 | 7458 |
| 40 and 176 | 880 |
| 194 and 67 | 12998 |
| 113 and 157 | 17741 |
| 92 and 120 | 2760 |