Least Common Multiple (LCM) of 121 and 84
The least common multiple (LCM) of 121 and 84 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 121 and 84?
First, calculate the GCD of 121 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 84 = 1 remainder 37 |
| 2 | 84 ÷ 37 = 2 remainder 10 |
| 3 | 37 ÷ 10 = 3 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 79 | 4819 |
| 158 and 131 | 20698 |
| 138 and 195 | 8970 |
| 199 and 27 | 5373 |
| 116 and 110 | 6380 |