Least Common Multiple (LCM) of 49 and 164
The least common multiple (LCM) of 49 and 164 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 49 and 164?
First, calculate the GCD of 49 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 164 = 0 remainder 49 |
| 2 | 164 ÷ 49 = 3 remainder 17 |
| 3 | 49 ÷ 17 = 2 remainder 15 |
| 4 | 17 ÷ 15 = 1 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 152 | 7448 |
| 180 and 57 | 3420 |
| 98 and 85 | 8330 |
| 93 and 153 | 4743 |
| 112 and 132 | 3696 |