Least Common Multiple (LCM) of 84 and 122
The least common multiple (LCM) of 84 and 122 is 5124.
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 122?
First, calculate the GCD of 84 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 122 = 0 remainder 84 |
| 2 | 122 ÷ 84 = 1 remainder 38 |
| 3 | 84 ÷ 38 = 2 remainder 8 |
| 4 | 38 ÷ 8 = 4 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 33 | 2046 |
| 53 and 77 | 4081 |
| 170 and 71 | 12070 |
| 181 and 79 | 14299 |
| 85 and 47 | 3995 |