Least Common Multiple (LCM) of 164 and 121
The least common multiple (LCM) of 164 and 121 is 19844.
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 164 and 121?
First, calculate the GCD of 164 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 121 = 1 remainder 43 |
| 2 | 121 ÷ 43 = 2 remainder 35 |
| 3 | 43 ÷ 35 = 1 remainder 8 |
| 4 | 35 ÷ 8 = 4 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 120 | 840 |
| 31 and 101 | 3131 |
| 79 and 99 | 7821 |
| 54 and 191 | 10314 |
| 133 and 171 | 1197 |