Least Common Multiple (LCM) of 164 and 43
The least common multiple (LCM) of 164 and 43 is 7052.
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 43?
First, calculate the GCD of 164 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 43 = 3 remainder 35 |
| 2 | 43 ÷ 35 = 1 remainder 8 |
| 3 | 35 ÷ 8 = 4 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 27 | 594 |
| 169 and 38 | 6422 |
| 54 and 53 | 2862 |
| 190 and 143 | 27170 |
| 45 and 41 | 1845 |