Least Common Multiple (LCM) of 164 and 107
The least common multiple (LCM) of 164 and 107 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 164 and 107?
First, calculate the GCD of 164 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 107 = 1 remainder 57 |
| 2 | 107 ÷ 57 = 1 remainder 50 |
| 3 | 57 ÷ 50 = 1 remainder 7 |
| 4 | 50 ÷ 7 = 7 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 52 | 7124 |
| 119 and 128 | 15232 |
| 63 and 144 | 1008 |
| 171 and 66 | 3762 |
| 179 and 181 | 32399 |