Least Common Multiple (LCM) of 100 and 164
The least common multiple (LCM) of 100 and 164 is 4100.
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 100 and 164?
First, calculate the GCD of 100 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 164 = 0 remainder 100 |
| 2 | 164 ÷ 100 = 1 remainder 64 |
| 3 | 100 ÷ 64 = 1 remainder 36 |
| 4 | 64 ÷ 36 = 1 remainder 28 |
| 5 | 36 ÷ 28 = 1 remainder 8 |
| 6 | 28 ÷ 8 = 3 remainder 4 |
| 7 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 17 | 3060 |
| 20 and 58 | 580 |
| 102 and 131 | 13362 |
| 185 and 12 | 2220 |
| 107 and 97 | 10379 |