Least Common Multiple (LCM) of 164 and 49
The least common multiple (LCM) of 164 and 49 is 8036.
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 49?
First, calculate the GCD of 164 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 49 = 3 remainder 17 |
| 2 | 49 ÷ 17 = 2 remainder 15 |
| 3 | 17 ÷ 15 = 1 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 169 | 19097 |
| 49 and 117 | 5733 |
| 105 and 15 | 105 |
| 70 and 65 | 910 |
| 54 and 77 | 4158 |