Least Common Multiple (LCM) of 107 and 164
The least common multiple (LCM) of 107 and 164 is 17548.
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 107 and 164?
First, calculate the GCD of 107 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 164 = 0 remainder 107 |
| 2 | 164 ÷ 107 = 1 remainder 57 |
| 3 | 107 ÷ 57 = 1 remainder 50 |
| 4 | 57 ÷ 50 = 1 remainder 7 |
| 5 | 50 ÷ 7 = 7 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 138 | 5106 |
| 115 and 69 | 345 |
| 176 and 29 | 5104 |
| 116 and 110 | 6380 |
| 59 and 178 | 10502 |