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 |
|---|---|
| 86 and 126 | 5418 |
| 61 and 85 | 5185 |
| 89 and 82 | 7298 |
| 185 and 136 | 25160 |
| 153 and 126 | 2142 |