Least Common Multiple (LCM) of 165 and 196
The least common multiple (LCM) of 165 and 196 is 32340.
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 165 and 196?
First, calculate the GCD of 165 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 196 = 0 remainder 165 |
| 2 | 196 ÷ 165 = 1 remainder 31 |
| 3 | 165 ÷ 31 = 5 remainder 10 |
| 4 | 31 ÷ 10 = 3 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 100 | 1900 |
| 119 and 193 | 22967 |
| 71 and 177 | 12567 |
| 25 and 170 | 850 |
| 152 and 10 | 760 |