Least Common Multiple (LCM) of 35 and 164
The least common multiple (LCM) of 35 and 164 is 5740.
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 35 and 164?
First, calculate the GCD of 35 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 164 = 0 remainder 35 |
| 2 | 164 ÷ 35 = 4 remainder 24 |
| 3 | 35 ÷ 24 = 1 remainder 11 |
| 4 | 24 ÷ 11 = 2 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 101 | 4242 |
| 188 and 132 | 6204 |
| 97 and 133 | 12901 |
| 22 and 120 | 1320 |
| 133 and 71 | 9443 |