Least Common Multiple (LCM) of 100 and 192
The least common multiple (LCM) of 100 and 192 is 4800.
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 192?
First, calculate the GCD of 100 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 192 = 0 remainder 100 |
| 2 | 192 ÷ 100 = 1 remainder 92 |
| 3 | 100 ÷ 92 = 1 remainder 8 |
| 4 | 92 ÷ 8 = 11 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 70 | 210 |
| 131 and 17 | 2227 |
| 19 and 110 | 2090 |
| 125 and 110 | 2750 |
| 188 and 108 | 5076 |