Least Common Multiple (LCM) of 100 and 165
The least common multiple (LCM) of 100 and 165 is 3300.
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 165?
First, calculate the GCD of 100 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 165 = 0 remainder 100 |
| 2 | 165 ÷ 100 = 1 remainder 65 |
| 3 | 100 ÷ 65 = 1 remainder 35 |
| 4 | 65 ÷ 35 = 1 remainder 30 |
| 5 | 35 ÷ 30 = 1 remainder 5 |
| 6 | 30 ÷ 5 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 140 | 4340 |
| 188 and 172 | 8084 |
| 110 and 19 | 2090 |
| 63 and 38 | 2394 |
| 197 and 32 | 6304 |