Least Common Multiple (LCM) of 84 and 121
The least common multiple (LCM) of 84 and 121 is 10164.
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 84 and 121?
First, calculate the GCD of 84 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 121 = 0 remainder 84 |
| 2 | 121 ÷ 84 = 1 remainder 37 |
| 3 | 84 ÷ 37 = 2 remainder 10 |
| 4 | 37 ÷ 10 = 3 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 12 | 2220 |
| 32 and 177 | 5664 |
| 122 and 86 | 5246 |
| 118 and 37 | 4366 |
| 30 and 122 | 1830 |