Least Common Multiple (LCM) of 164 and 100
The least common multiple (LCM) of 164 and 100 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 164 and 100?
First, calculate the GCD of 164 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 100 = 1 remainder 64 |
| 2 | 100 ÷ 64 = 1 remainder 36 |
| 3 | 64 ÷ 36 = 1 remainder 28 |
| 4 | 36 ÷ 28 = 1 remainder 8 |
| 5 | 28 ÷ 8 = 3 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 13 | 1365 |
| 168 and 136 | 2856 |
| 15 and 190 | 570 |
| 93 and 144 | 4464 |
| 188 and 120 | 5640 |